Entanglement spectrum of a topological phase in one dimension

Abstract

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of $\pi$-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.

11 pages, 4 figures, references added, minor corrections, meta data updated

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• Detecting subsystem symmetry protected topological order via entanglement entropy
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Preparing quantum many-body scar states on quantum computers
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• New gapped quantum phases for S=1 spin chain with D2h symmetry
• Quantum simulation of entanglement and hadronization in jet production: lessons from the massive Schwinger model
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Fate of exceptional points under interactions: Reduction of topological classifications
• Unwinding Short-Range Entanglement
• Hidden order and symmetry protected topological states in quantum link ladders
• Bond Order via Light-Induced Synthetic Many-body Interactions of Ultracold Atoms in Optical Lattices
• Topological phases in odd-legs frustrated synthetic ladders
• Quantum phase transition and critical behavior between the gapless topological phases
• Out-of-equilibrium dynamics and thermalization of string order
• Topological and dynamical properties of a generalized cluster model in one dimension
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Condensed Matter Applications of Entanglement Theory
• Fermions with cubic and quartic spectrum
• Supersolid-Superfluid phase separation in the extended Bose-Hubbard model
• `Gauging' time reversal symmetry in tensor network states
• Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy
• Thermalization in Systems with Bipartite Eigenmode Entanglement
• Symmetry Protected Quantum State Renormalization
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Topological Bootstrap: Fractionalization From Kondo Coupling
• Designing quantum many-body matter with conditional generative adversarial networks
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Topological Order Parameters of the Spin-1/2 Dimerized Heisenberg Ladder in Magnetic Field
• Fractional corner charges in a 2D super-lattice Bose-Hubbard model
• Emergence of Superconductivity in Doped Multiorbital Hubbard Chains
• Haldane Topological Orders in Motzkin Spin Chains
• Emergent conformal boundaries from finite-entanglement scaling in matrix product states
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• Folding approach to topological orders enriched by mirror symmetry
• Full counting statistics and the Edgeworth series for matrix product states
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Homotopical Foundations of Parametrized Quantum Spin Systems
• Weakly coupled alternating $S=1/2$ chains in the distorted honeycomb lattice compound Na${}_2$Cu${}_2$TeO${}_6$
• Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires
• Recent progress on quantum simulations of non-standard Bose-Hubbard models
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Universal entanglement spectra in critical spin chains
• Impurity bound states as detectors of topological band structures revisited
• Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
• Entanglement estimation in tensor network states via sampling
• Topological Phases of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain with Frustrated Next-Nearest-Neighbour Interaction
• Continuous phase transition between bosonic integer quantum Hall liquid and trivial insulator: evidences for deconfined quantum criticality
• The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Bosonic symmetry protected topological phases with reflection symmetry
• Hubbard model for spin-1 Haldane chains
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation
• Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy
• Visualizing Quasiparticles from Quantum Entanglement for general 1D phases
• Quantum phase transitions in the dimerized extended Bose-Hubbard model
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Brane parity orders in the insulating state of Hubbard ladders
• Control of Magnetic and Topological Orders with a DC Electric Field
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Critical theory of the topological quantum phase transition in a spin-2 chain
• Detecting the critical point through entanglement in Schwinger model
• Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
• Simulating topological tensor networks with Majorana qubits
• Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly-interacting to the non-interacting limit
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Symmetry-protected topological order in magnetization plateau states of quantum spin chains
• Tensor Network Implementation of Bulk Entanglement Spectrum
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator
• Disentangling quantum matter with measurements
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Effective spin chains for fractional quantum Hall states
• From observations to complexity of quantum states via unsupervised learning
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Destruction of string order after a quantum quench
• Emergent particles and gauge fields in quantum matter
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Haldane insulator protected by reflection symmetry in the doped Hubbard model on the three-legged ladder
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• Entanglement Spectrum of a Random Partition: Connection with the Localization Transition
• (SPT-)LSM theorems from projective non-invertible symmetries
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• Estimating localizable entanglement from witnesses
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
• Topological disentangler for the valence-bond-solid chain
• Holonomic quantum computing in symmetry-protected ground states of spin chains
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Criticality at the Haldane-insulator charge-density-wave quantum phase transition
• Kramers' degeneracy for open systems in thermal equilibrium
• Relativistic continuous matrix product states for quantum fields without cutoff
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Matrix product states for topological phases with parafermions
• Deconfining disordered phase in two-dimensional quantum link models
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Spin-1 models in the ultrastrong coupling regime of circuit QED
• Entanglement in a second order topological insulator on a square lattice
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Entanglement spectrum of mixed states
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
• Optimization schemes for unitary tensor-network circuit
• Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain
• Surface field theories of point group symmetry protected topological phases
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Duality viewpoint of criticality
• All spin-1 topological phases in a single spin-2 chain
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Interaction induced fractionalization and topological superconductivity in the polar molecules anisotropic $t-J$ model
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Entanglement analysis of isotropic spin-1 chains
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Ground-state phase diagram of the frustrated spin-1/2 two-leg honeycomb ladder
• Tensor renormalization group in bosonic field theory
• An algorithm to explore entanglement in small systems
• Topological quantum synchronization of fractionalized spins
• High-frequency Expansion for Floquet Prethermal Phases with Emergent Symmetries: Application to Time Crystals and Floquet Engineering
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Bosonic integer quantum Hall effect as topological pumping
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Effective field theories of topological crystalline insulators and topological crystals
• Interaction-induced topological phase transition at finite temperature
• Edge modes and symmetry-protected topological states in open quantum systems
• Irreducible Projective Representations and Their Physical Applications
• Altermagnetic Instabilities from Quantum Geometry
• Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
• Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
• Topology and the one-dimensional Kondo-Heisenberg model
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Characterization of a correlated topological Kondo insulator in one dimension
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Finite Size Scaling of Topological Entanglement Entropy
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Nonclassicality and criticality in symmetry-protected magnetic phases
• Inaccessible entanglement in symmetry protected topological phases
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain
• Transmission through a potential barrier in Luttinger liquids with a topological spin gap
• Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction
• Symmetry protected gapless $Z_2$ spin liquids
• Long-range entanglement and topological excitations
• Multimagnon dynamics and thermalization in the $S=1$ easy-axis ferromagnetic chain
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model
• Symmetry-protected topological phase in a one-dimensional correlated bosonic model with a synthetic spin-orbit coupling
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Constructing the spin-1 Haldane phase on a qudit quantum processor
• Topological Devil's staircase in atomic two-leg ladders
• Density-induced geometric frustration of ultra-cold bosons in optical lattices
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• Non universality of entanglement convertibility
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions
• Highly entangled stationary states from strong symmetries
• Modified spin-wave theory and spin liquid behavior of cold bosons on an inhomogeneous triangular lattice
• Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise
• Hidden Magnetism in Periodically Modulated One Dimensional Dipolar Fermions
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Gapless edge states and their stability in two-dimensional quantum magnets
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Symmetry protected phases in inhomogeneous spin chains
• Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization
• Long-range nonstabilizerness and phases of matter
• Entanglement properties of the Haldane phases: A finite system-size approach
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Detecting phase boundaries of quantum spin-1/2 XXZ ladder via bipartite and multipartite entanglement transitions
• Quantum reservoir probing of quantum phase transitions
• Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Vector-spin-chirality order in a dimerized frustrated spin-1/2 chain
• Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band
• The split and approximate split property in 2D systems: stability and absence of superselection sectors
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Integrable spin chains and the Clifford group
• Homogeneous and domain wall topological Haldane conductors with dressed Rydberg atoms
• Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains
• Quantum phase transitions and string orders in the spin-1/2 Heisenberg-Ising alternating chain with Dzyaloshinskii-Moriya interaction
• Topological chiral currents in the Gross-Neveu model extension
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Entanglement properties of spin models in triangular lattices
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Phase diagrams of spin-$S$ Kitaev ladders
• Entanglement Dynamics of the Non-Unitary Holographic Channel
• Spin-1 Haldane phase in a chain of Rydberg atoms
• Entanglement Driven Phase Transitions in Spin-Orbital Models
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Renormalization group approach to symmetry protected topological phases
• Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
• Quantum phase transitions of topological insulators without gap closing
• One-dimensional repulsive Hubbard model with mass imbalance: Orders and filling anomaly
• Characterization of Topological Phases of Spin-1/2 Frustrated Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chains by Entanglement Spectrum
• Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks
• Resonating dimer-monomer liquid state in a magnetization plateau of a spin-$\frac{1}{2}$ kagome-strip Heisenberg chain
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Density matrix renormalization group study in energy space for a single-impurity Anderson model and an impurity quantum phase transition
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Exact zero modes in frustrated Haldane chains
• Correlation-Assisted Quantized Charge Pumping
• Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data
• Automorphic equivalence preserves the split property
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian
• Comparative study of the density matrix embedding theory for the Hubbard models
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• Numerical detection of symmetry enriched topological phases with space group symmetry
• Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits
• Plateau transitions of spin pump and bulk-edge correspondence
• Control of superexchange interactions with DC electric fields
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation on a frustrated ferromagnetic spin-$1/2$ chain
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches
• Exact projected entangled pair ground states with topological Euler invariant
• Islands of Chiral Solitons in Integer Spin Kitaev Chains
• Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Local entanglement and String Order Parameter in dimerized models
• Unitary Designs of Symmetric Local Random Circuits
• Cumulants and Scaling Functions of Infinite Matrix Product States
• Identifying quantum phases from injectivity of symmetric matrix product states
• Long-range magnetic order and interchain interactions in the $S=2$ chain system MnCl${}_3$(bpy)
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Topological obstructed atomic limit by annihilating Dirac fermions
• Disorder-induced topology in quench dynamics
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• Transition to the Haldane phase driven by electron-electron correlations
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains
• A unified diagrammatic approach to topological fixed point models
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Dissipative Symmetry-Protected Topological Order
• Charting the space of ground states with tensor networks
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Microscopic model for the semiconductor-to-ferromagnetic-metal transition in FeSi${}_{1-x}$Ge${}_x$ Alloys
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Many-body entanglement and topology from uncertainties and measurement-induced modes
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Macroscopic boundary effects in the one-dimensional extended Bose-Hubbard model
• Efficient variational quantum circuit structure for correlated topological phases
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Characterization of randomness in quantum circuits of continuous gate sets
• Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Critical behavior of the extended Hubbard model with bond dimerization
• Sign structure and ground state properties for a spin-$S$ $t$-$J$ chain
• Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Entanglement in non-critical inhomogeneous quantum chains
• Classification of trivial spin-1 tensor network states on a square lattice
• Magnetization plateau of the $S=2$ antiferromagnetic Heisenberg chain with anisotropies
• Symmetry-protected intermediate trivial phases in quantum spin chains
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• Typical entanglement entropy in systems with particle-number conservation
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Reentrance of Topological Phase in Spin-1 Frustrated Heisenberg Chain
• Theory of quantum kagome ice and vison zero modes
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• Role of conservation laws in the Density Matrix Renormalization Group
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution
• Squashed entanglement in one-dimensional quantum matter
• Geometric Approach to 3D Interfaces at Strong Coupling
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Ground-State Phase Diagram of the Bond-Alternating $S=2$ Quantum Spin Chain with the $XXZ$ and On-Site Anisotropies -- Symmetry Protected Topological Phase versus Trivial Phase
• Robust symmetry-protected metrology with the Haldane phase
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Microscopic model for magneto-electric coupling through lattice distortions
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Interaction quench and thermalization in a one-dimensional topological Kondo insulator
• Pivoting through the chiral-clock family
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Introduction to quantum entanglement in many-body systems
• Magnetic field-dependent dynamics and field-driven metal-to-insulator transition of the half-filled Hubbard model: A DMFT+DMRG study
• Magnetic phase diagrams of the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain: Emergence of a Haldane phase
• Entanglement entropy and fidelity susceptibility in the one-dimensional spin-1 XXZ chains with alternating single-site anisotropy
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Electronic structure, magnetic properties and pairing tendencies of the copper-based honeycomb lattice Na${}_2$Cu${}_2$TeO${}_6$
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Composite symmetry protected topological order and effective models
• Entanglement in 3D Kitaev Spin Liquids
• Topological phases in two-legged Heisenberg ladders with alternating interactions
• Dynamical probing of a topological phase of bosons in one dimension
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Topological phase transition and the effect of Hubbard interaction on the one-dimensional topological Kondo insulator
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Non-local Order Parameters and Quantum Entanglement for Fermionic Topological Field Theories
• Topological phases arising from attractive interaction and pair hopping in the Extended Hubbard Model
• Competition between Hund's coupling and Kondo effect in a one-dimensional extended periodic Anderson model
• Resilience of hidden order to symmetry-preserving disorder
• Complex entanglement entropy for complex conformal field theory
• Entanglement gap, corners, and symmetry breaking
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• Schmidt gap in random spin chains
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Finite entanglement properties in the matrix product states of the one-dimensional Hubbard model
• Quantum phase transitions in spin-1 compass chains
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Synthetic Hall tube of interacting fermions
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Excitonic Correlations, Spin-State Ordering, and Magnetic-Field Effects in One-Dimensional Two-Orbital Hubbard Model for Spin-Crossover Region
• Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1^{\prime }$-$J_2$ chain
• Symmetry protected topological phases in spin-1 ladders and their phase transitions
• State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
• Observation of average topological phase in disordered Rydberg atom array
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• Gauge theory and mixed state criticality
• Floquet Flux Attachment in Cold Atomic Systems
• Variational Tensor Network Operator
• Invariance of topological indices under Hilbert space truncation
• Can multipartite entanglement be characterized by two-point connected correlation functions ?
• String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems
• Phase diagram of spin-$1$ chains with Dzyaloshinskii-Moriya interaction
• Duality and Stacking of Bosonic and Fermionic SPT Phases
• Self-$G$-ality in 1+1 dimensions
• Boundary States as Holographic Duals of Trivial Spacetimes
• Discrete symmetries and Lieb-Schultz-Mattis theorem
• Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure
• Exact correlations in topological quantum chains
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Exact results for the entanglement in 1D Hubbard models with spatial constraints
• Symmetry classification of typical quantum entanglement
• Infinite-size density matrix renormalization group with parallel Hida's algorithm
• Quantum criticality in dimerised anisotropic spin-1 chains
• Quantum Simulation of Spin-1 XXZ-Heisenberg Models and the Haldane Phase with Dysprosium
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Topological physics in quantum critical systems
• Phase transitions in the one-dimensional ionic Hubbard model
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• The low-energy TQFT of the generalized double semion model
• Renormalization view on resonance proliferation between many-body localized phases
• Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains
• Preparing matrix product states via fusion: constraints and extensions
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Characterization of helical states in semiconductor quantum wells using quantum information quantities
• Distilling momentum-space entanglement in Luttinger liquids at finite temperature
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Intersublattice entanglement entropy as an extensive property in antiferromagnets
• Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain
• Composite Quantum Phases in Non-Hermitian Systems
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Ground states of one-dimensional dipolar lattice bosons at unit filling
• Solvable lattice model for (2+1)D bosonic topological insulator
• Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
• Quantum teleportation implies symmetry-protected topological order
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Two-dimensional Paired Topological Superfluids of Rydberg Fermi Gases
• Unwinding of a one-dimensional topological superconductor
• Topological quantum phase transitions in a Majorana chain with spatial modulation
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Multiparticle quantum walk: a dynamical probe of topological many-body excitations
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Topological self-organization of strongly interacting particles
• Bosonic Integer Quantum Hall States without Landau Levels on Square Lattice
• Topological quantum phase transition in strongly correlated Kondo insulators in 1D
• Quantum order by disorder in Frustrated Spin Nanotubes
• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
• Quasi-fractionalization of spin in a cluster-based Haldane state supported by chirality of a triangular spin tube
• Tensor Renormalization Group for interacting quantum fields
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Understanding and utilizing the inner bonds of process tensors
• Self-organization in many-body systems with short-range interactions: clustering, correlations and topology
• Fractional domain wall statistics in spin chains with anomalous symmetries
• Topological Superconductivity in Doped Symmetry Protected Topological State
• Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase
• The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
• Competition between dimerization and vector chirality in the spin-$3/2$ $J_1$-$J_2$ Heisenberg chain with uniaxial single-ion anisotropy
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Complete characterization of spin chains with two Ising symmetries
• Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints
• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains
• Deconfined criticality as intrinsically gapless topological state in one dimension
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain
• Relaxation of the entanglement spectrum in quench dynamics of topological systems
• Matrix product states for $su(2)$ invariant quantum spin chains
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Quantum simulation of superexchange magnetism in linear ion crystals
• On integrable matrix product operators with bond dimension $D=4$
• Field theory analysis of S=1 antiferromagnetic bond-alternating chains in the dimer phase
• Entanglement, subsystem particle numbers and topology in free fermion systems
• One-dimensional symmetric phases protected by frieze symmetries
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• A Classifying Space for Phases of Matrix Product States
• Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• A Simple and General Equation for Matrix Product Unitary Generation
• Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Revealing the topological nature of the bond order wave in a strongly correlated quantum system
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Distribution of entanglement Hamiltonian spectrum in free fermion models
• Topological Dipole Insulator
• Topological term in the non-linear $\sigma$ model of the SO(5) spin chains
• Scaling of entanglement entropy at quantum critical points in random spin chains
• Mass ratio of elementary excitations in frustrated antiferromagnetic chains with dimerization
• Translational Symmetry Broken Magnetization Plateau of the $S=2$ Antiferromagnetic Chain with Anisotropies
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Parity-dependent phase diagrams in spin-cluster two-leg ladders
• Hidden $SU(2)$ Symmetries, the Symmetry Hierarchy and the Emergent Eight-Fold Way in Spin-1 Quantum Magnets
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice
• Partially topological phase in a quantum loop gas model with tension and pressure
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Spectroscopic Feature of Quantum Many-Body Scar States
• Quantum Restored Symmetry Protected Topological Phases
• Topological Phase Diagram of Generalized SSH Models with Interactions
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Emergent infinite-randomness fixed points from the extensive random bipartitions of the spin-1 Affleck-Kennedy-Lieb-Tasaki topological state
• Quantum phase with spontaneous translational symmetry breaking in an extended diamond chain
• Instanton effects in lattice models of bosonic symmetry-protected topological states
• A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas
• Entropic order parameters and topological holography
• Simulating Topological Order on Quantum Processors
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Entanglement distance between quantum states and its implications for density-matrix-renormalization-group study of degenerate ground-states
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Topological Phases of Spin-1/2 Ferromagnetic--Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Topological Phase Transition in the Two-Leg Hubbard Model: Emergence of the Haldane Phase via Diagonal Hopping and Strong Interactions
• $N$-ality symmetry and SPT phases in (1+1)d
• Quantum Degenerate Majorana Surface Zero Modes in Two-Dimensional Space
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Post-measurement Quantum Monte Carlo
• Threefold Way for Typical Entanglement
• Entanglement gap in 1D long-range quantum spherical models
• Entanglement detachment in fermionic systems
• Emergence of topological states in relaxation dynamics of interacting bosons
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Interrelations among frustration-free models via Witten's conjugation
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Angular-time evolution for the Affleck-Kennedy-Lieb-Tasaki chain and its edge-state dynamics
• S=2 Quantum Spin Chain with the Biquadratic Exchange Interaction
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Entanglement-enabled symmetry-breaking orders
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Topological phases of the compass ladder model
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Construction of Entangled Many-body States via the Higgs Mechanism
• Extended Ashkin-Teller transition in two coupled frustrated Haldane chains
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group
• Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism
• Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Topological floating phase of dipolar bosons in an optical ladder
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Layer-number parity induced topological phase transition
• Entanglement Spectrum Resolved by Loop Symmetries
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
• Energetical self-organization of a few strongly interacting particles
• Dynamical Geometry of the Haldane Model under a Quantum Quench
• Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition
• Ground-State Phase Diagram of an Anisotropic S=1 Ferromagnetic-Antiferromagnetic Bond-Alternating Chain
• Geometric Effects on Tunneling in Driven Quantum Systems
• Survival of Hermitian Criticality in the Non-Hermitian Framework
• Tensor network states for the description of quantum many-body systems
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems
• Anisotropy-induced spin parity effects
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Quantum cluster kink and ring frustration
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Unveiling topological order through multipartite entanglement
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Learning Variational Quantum Circuit Parameters with Classical Artificial Intelligence for Quantum Phase Transition Detection
• Higher-order topological quantum paramagnets
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Spurious Strange Correlators in Symmetry-Protected Topological Phases
• Spin order, spin excitations, and RIXS spectra of spin-1/2 tetramer chains
• Electrostatically-induced topological phase transitions in polyacetylene molecules
• Topological phases of bosons with local parity coupling on a dimerized lattice
• Detection of 2D SPT Order with Partial Symmetries
• One-dimensional interacting Su-Schrieffer-Heeger model at quarter filling: An exact diagonalization study
• Non-Abelian Charge Transport in Three-Flavor Gauge Semimetal Model with Braiding Majoranas
• Dynamically generated quadrupole polarization using Floquet adiabatic evolution
• Tensorization of neural networks for improved privacy and interpretability
• Persistent Haldane Phase in Carbon Tetris Chains
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Magnetically tuned topological phase in graphene nanoribbon heterojunctions
• Bosonic Haldane insulator in the presence of local disorder: A quantum Monte Carlo study
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Entanglement entropy as a probe of topological phase transitions
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains
• Bosonic realization of SU(3) chiral Haldane phases
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Undecidability of the spectral gap in rotationally symmetric Hamiltonians