Identifying Topological Order by Entanglement Entropy

Abstract

Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the Topological Entanglement Entropy (TEE) using the Density Matrix Renormalization Group (DMRG). We argue that the DMRG algorithm naturally produces a minimally entangled state, from amongst the quasi-degenerate ground states in a topological phase. This proposal both explains the success of this method, and the absence of ground state degeneracy found in prior DMRG sightings of topological phases. We demonstrate the effectiveness of the calculational procedure by obtaining the TEE for several microscopic models, with an accuracy of order $10^{-3}$ when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show the ground state of the quantum $S=1/2$ antiferromagnet on the kagomé lattice is a topological spin liquid, and strongly constrain the full identification of this phase of matter.

20 pages, 6 figures

References in corpus (15)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Low-energy effective theory of the toric code model in a parallel field
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Quantum phase transitions of antiferromagnets and the cuprate superconductors

Cited by in corpus (499)

• Quantum Spin Liquids
• Quantum Spin Liquid States
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum entanglement in condensed matter systems
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Topological Flat Band Models and Fractional Chern Insulators
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• The Hubbard Model
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• A classification of symmetry enriched topological phases with exactly solvable models
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Unusual ordered phases of highly frustrated magnets: a review
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Entanglement Temperature and Entanglement Entropy of Excited States
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Experimental identification of quantum spin liquids
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• A Short Introduction to Topological Quantum Computation
• Characterizing topological order by studying the ground states of an infinite cylinder
• Correlation effects in two-dimensional topological insulators
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Theory of defects in Abelian topological states
• Lecture Notes of Tensor Network Contractions
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Dynamical Time-Reversal Symmetry Breaking and Photo-Induced Chiral Spin Liquids in Frustrated Mott Insulators
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Universal behavior beyond multifractality in quantum many-body systems
• Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice
• Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS${}_2$
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Matrix Product State applications for the ALPS project
• Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu${}_3$(OH)${}_6$Cl${}_2$
• Classification of subsystem symmetry-protected topological phases
• Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
• Witnessing entanglement in quantum magnets using neutron scattering
• Nature of chiral spin liquids on the kagome lattice
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• A Quantum Dipolar Spin Liquid
• One-Third Magnetization Plateau with a Preceding Novel Phase in Volborthite
• Scaling of entanglement entropy at deconfined quantum criticality
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Spurious topological entanglement entropy from subsystem symmetries
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Spin Thermal Hall Conductivity of a Kagomé Antiferromagnet
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Quantum spin-liquid behavior in the spin-1/2 random-bond Heisenberg antiferromagnet on the kagome lattice
• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Renormalization group analysis of competing quantum phases in the J1-J2 Heisenberg model on the kagome lattice
• Quantum Magnetism in Minerals
• Matrix Product States for Trial Quantum Hall States
• A Class of Compounds Featuring Frustrated Triangular Magnetic Lattice CsRESe${}_2$ (RE=La-Lu): Quantum Spin-Liquid Candidates
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Spurious Long-range Entanglement and Replica Correlation Length
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Unconventional Magnetic Ground State in Yb${}_2$Ti${}_2$O${}_7$
• Constraints on topological order in Mott Insulators
• Possible Dirac quantum spin liquid in a kagome quantum antiferromagnet YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]
• An invariant of topologically ordered states under local unitary transformations
• Unifying approach to the quantification of bipartite correlations by Bures distance
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• The mother of all states of the kagome quantum antiferromagnet
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Chiral projected entangled-pair state with topological order
• Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
• Entanglement topological invariants for one-dimensional topological superconductors
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Haydeeite: a spin-1/2 kagome ferromagnet
• Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Numerical study of a transition between Z2 topologically ordered phases
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Detecting two dimensional symmetry protected topological order in a ground state wave function
• Optimized contraction scheme for tensor-network states
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Entanglement signatures of emergent Dirac fermions: kagome spin liquid & quantum criticality
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice
• Coherent Transmutation of Electrons into Fractionalized Anyons
• Chiral spin liquids on the kagome Lattice
• Ultrafast renormalization of the onsite Coulomb repulsion in a cuprate superconductor
• Genuine Multipartite Entanglement in the $XY$ Model
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Growth of mutual information in a quenched one-dimensional open quantum many body system
• Quantum Spin Liquid in a Breathing Kagome Lattice
• Materializing Rival Ground States in the Barlowite Family of Kagome Magnets: Quantum Spin Liquid, Spin Ordered, and Valence Bond Crystal States
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Spectroscopic signatures of crystal momentum fractionalization
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid
• Thermal Hall Effects of Spins and Phonons in Kagome Antiferromagnet Cd-Kapellasite
• Quantum spin liquids in the absence of spin-rotation symmetry: application to Herbertsmithite
• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Non-unitary operations for ground-state calculations in near term quantum computers
• Obtaining topological degenerate ground states by the density matrix renormalization group
• Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Scaling Theory of Topological Phase Transitions
• Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands
• Bounds on corner entanglement in quantum critical states
• Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
• Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 $J_1-J_2$ XY Model on the Honeycomb Lattice
• Spinon Fractionalization from Dynamic Structure Factor of Spin-1/2 Heisenberg Antiferromagnet on the Kagome Lattice
• Dynamic fingerprint of fractionalized excitations in single-crystalline Cu${}_3$Zn(OH)${}_6$FBr
• Quantum spin liquid in the semiclassical regime
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet
• Experimentally Probing Topological Order and Its Breakdown via Modular Matrices
• Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
• Universal aspects in the behavior of the entanglement spectrum in one dimension: scaling transition at the factorization point and ordered entangled structures
• Heat Transport in Herbertsmithite: Can a Quantum Spin Liquid Survive Disorder?
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
• Crystalline Kitaev spin liquids
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model
• Effect of Zn doping on the antiferromagnetism in kagome Cu${}_{4-x}$Zn${}_x$(OH)${}_6$FBr
• Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
• Striped spin liquid crystal ground state instability of kagome antiferromagnets
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Entanglement patterns and generalized correlation functions in quantum many body systems
• Spin liquid versus dimer phases in an anisotropic J1-J2 frustrated square antiferromagnet
• Entanglement Spectroscopy using Quantum Monte Carlo
• End states in a 1-D topological Kondo insulator
• Topological Disorder Parameter
• Bulk-edge correspondence in fractional Chern insulators
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Topological Nematic Spin Liquid on the Square-Kagome Lattice
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Unification of bosonic and fermionic theories of spin liquids on the kagome lattice
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• $ab$-$initio$ Approaches for Low-Energy Spin Hamiltonians
• Heat transport of the kagomé Heisenberg quantum spin liquid candidate YCu${}_3$(OH)${}_{6.5}$Br${}_{2.5}$: localized magnetic excitations and spin gap
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• Strong correlation induced charge localization in antiferromagnets
• The Entanglement Entropy between Short Range Correlations and the Fermi Sea in Nuclear Structure
• Emergent spin-gapped magnetization plateaus in a spin-1/2 perfect kagome antiferromagnet
• Investigating Topological Order using Recurrent Neural Networks
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Instabilities of Spin-Liquid States in a Quantum Kagome Antiferromagnet
• Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Kitaev Quantum Spin Liquids
• Kagome-Triangular Lattice Antiferromagnet NaBa2Mn3F11
• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Kagome chiral spin liquid as a gauged U(1) symmetry protected topological phase
• Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model
• Phase diagram of the 1/3-filled extended Hubbard model on the Kagome lattice
• Anyonic Entanglement and Topological Entanglement Entropy
• Variational study of the ground state and spin dynamics of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model and its implication on Hebertsmithite ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Entanglement bootstrap approach for gapped domain walls
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Doping quantum spin liquids on the Kagome lattice
• Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice
• Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature
• A DMRG study: Pair-density wave in spin-valley locked systems
• Scaling of entanglement entropy across Lifshitz transitions
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
• Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain
• Spin structure factors of chiral quantum spin liquids on the kagome lattice
• Interplay of charge and spin fluctuations of strongly interacting electrons on the kagome lattice
• Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• NMR study of the spin excitations in the frustrated antiferromagnet Yb(BaBO${}_3$)${}_3$ with a triangular lattice
• Typical and extreme entropies of long-lived isolated quantum systems
• Global Phase Diagram of D-wave Superconductivity in the Square-Lattice $t\text{-}J$ Model
• $\mu$SR Insight into the Impurity Problem in Quantum Kagome Antiferromagnets
• Capacity of Entanglement for Non-local Hamiltonian
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Transition between algebraic and ${\mathbb{Z}}_2$ quantum spin liquids at large $N$
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Automatically Differentiable Quantum Circuit for Many-qubit State Preparation
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Nature of the 1/9-magnetization plateau in the spin-1/2 kagome Heisenberg antiferromagnet
• Witnessing nonequilibrium entanglement dynamics in a strongly correlated fermionic chain
• Universal lower bound on topological entanglement entropy
• Dynamical disentangling and cooling of atoms in bilayer optical lattices
• Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
• Many-body entanglement in a topological chiral ladder
• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Scaling of the entanglement spectrum in driving critical dynamics
• Magnetization plateaus of an easy-axis Kagomé antiferromagnet with extended interactions
• Strain-induced pseudomagnetic field and quantum oscillations in kagome crystals
• Non-Symmetry-Breaking Ground State of the S=1 Heisenberg Model on the Kagome lattice
• Entanglement dynamics following a sudden quench: an exact solution
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Phenomenological Z_2 lattice gauge theory of the spin-liquid state of the kagome Heisenberg antiferromagnet
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Possible superconductivity with Bogoliubov Fermi surface in lightly doped Kagome U(1) spin liquid
• On Enriching the Levin-Wen model with Symmetry
• Kagome chiral spin liquid in transition metal dichalcogenide moiré bilayers
• Magnetic structure and high-field magnetization of the distorted kagome lattice antiferromagnet Cs${}_2$Cu${}_3$SnF${}_{12}$
• Gapless spin liquids in disguise
• Spin-1/2 Heisenberg antiferromanget on kagome: a $Z_2$ spin liquid with fermionic spinons
• Topological and dynamical properties of a generalized cluster model in one dimension
• Variational Monte Carlo Study of the 1/9 Magnetization Plateau in Kagome Antiferromagnets
• Resonating quantum three-coloring wavefunctions for the kagome quantum antiferromagnet
• Oscillating terms in the Renyi entropy of Fermi liquids
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Featureless quantum spin liquid, 1/3-magnetization plateau state and exotic thermodynamic properties of spin-1/2 frustrated Heisenberg antiferromagnet on an infinite Husimi lattice
• Staircase of crystal phases of hard-core bosons on the Kagome lattice
• Robustness of Topological Order in the Toric Code with Open Boundaries
• Variety of order-by-disorder phases in the asymmetric $J_1-J_2$ zigzag ladder: From the delta chain to the $J_1-J_2$ chain
• Multipartite entanglement in the 1-D spin-$\frac{1}{2}$ Heisenberg Antiferromagnet
• Quantifying entanglement with scattering experiments
• Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field
• Entanglement entropy in a periodically driven quantum Ising chain
• Kagome model for a ${\mathbb{Z}}_2$ quantum spin liquid
• Detecting Topological Order with Ribbon Operators
• Entanglement classification with matrix product states
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Antiferromagnetism, $f$-wave and chiral $p$-wave superconductivity in a Kagome lattice with possible application to $s{d}^2$-graphenes
• Cornering gapless quantum states via their torus entanglement
• On Arithmetic Modular Categories
• Detecting the critical point through entanglement in Schwinger model
• How correlations change the magnetic structure factor of the kagome Hubbard model
• How much entanglement can be created in a closed system?
• Heisenberg antiferromagnet on the Husimi lattice
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Accuracy of topological entanglement entropy on finite cylinders
• Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands
• Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Boson condensation and instability in the tensor network representation of string-net states
• Entanglement entropy as an order parameter for strongly coupled nodal line semimetals
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Global entanglement in a topological quantum phase transition
• Double-semion topological order from exactly solvable quantum dimer models
• Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Possible chiral spin liquid state in the $S=1/2$ kagome Heisenberg model
• Quantum Phase Transition between Z2 spin liquid and columnar Valence Bond Crystals on a Triangular lattice
• Antiferromagnetic spin-frustrated layers of corner-sharing Cu4 tetrahedra on the kagome lattice in volcanic minerals Cu5O2(VO4)2(CuCl), NaCu5O2(SeO3)2Cl3, and K2Cu5Cl8(OH)4 2H2O
• Estimating localizable entanglement from witnesses
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Diagnosing Topological Edge States via Entanglement Monogamy
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
• Engineering topological states and quantum-inspired information processing using classical circuits
• Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs${}_2$Cu${}_3$SnF${}_{12}$ and Rb${}_2$Cu${}_3$SnF${}_{12}$
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Extracting many-particle entanglement entropy from observables using supervised machine learning
• Asymmetric melting of one-third plateau in kagome quantum antiferromagnets
• Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Magnetic ground states in kagome YCu${}_3$(OH)${}_6$[(Cl${}_x$Br${}_{1-x}$)${}_{3-y}$(OH)${}_y$]
• Antiferromagnetism in kagome $\alpha$-Cu${}_3$Mg(OH)${}_6$Br${}_2$
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Renyi entropies for classical stringnet models
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Quantum Phases of Kagome Electron System with Half-Filled Flat Bands
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Spectrum of conformal gauge theories on a torus
• Long-range entanglement and topological excitations
• Evidence for the topological order in a kagome antiferromagnet
• Identifying non-Abelian topological ordered state and transition by momentum polarization
• Field-induced superfluids and Bose liquids in Projected Entangled Pair States
• Uhlmann fidelities from tensor networks
• Finite Size Scaling of Topological Entanglement Entropy
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• Measures of entanglement in non-Abelian anyonic systems
• An Operational Definition of Topological Order
• Dynamics of Pseudoentanglement
• Determining non-Abelian topological order from infinite projected entangled pair states
• Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
• Three-dimensional nematic spin liquid in the stacked triangular lattice 6H-B structure
• High energy spin excitations in the quantum spin liquid candidate Zn-barlowite probed by resonant inelastic x-ray scattering
• Optical conductivity of visons in Z2 spin liquids close to a VBS transition on the kagome lattice
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Entanglement dualities in supersymmetry
• Gauge field entanglement of Kitaev's honeycomb model
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Modified spin-wave theory and spin liquid behavior of cold bosons on an inhomogeneous triangular lattice
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Competing emergent Potts orders and possible nematic spin liquids in the Kagome $J_1-J_3$ Heisenberg model
• Destroying a topological quantum bit by condensing Ising vortices
• Spin, orbital and topological order in models of strongly correlated electrons
• Quantum probing topological phase transitions by non-Markovianity
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations
• Renyi Entropy of Interacting Thermal Bosons in Large $N$ Approximation
• Topological entanglement entropy of interacting disordered zigzag graphene ribbons
• Entanglement sum rules in exactly solvable models
• How quantum phases on cylinders approach the 2d limit
• Interspecies entanglement with impurity atoms in a lattice gas
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
• Lattice Laughlin states on the torus from conformal field theory
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2
• Local entanglement and String Order Parameter in dimerized models
• Vector boson excitations near deconfined quantum critical points
• Determining topological order from infinite projected entangled pair states
• Entanglement Entropy Near Kondo-Destruction Quantum Critical Points
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• Predicting topological quantum phase transition from dynamics via multisite entanglement
• An analog of topological entanglement entropy for mixed states
• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
• Classical criticality establishes quantum topological order
• Many-body entanglement and topology from uncertainties and measurement-induced modes
• Helical superfluid in a frustrated honeycomb Bose-Hubbard model
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• A Rényi entropy perspective on topological order in classical toric code models
• Correlation functions and quantum measures of descendant states
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Variational identification of a fractional Chern insulator in an extended Bose-Hubbard model
• Spinon quantum spin Hall state in the kagome antiferromagnet with a Dzyaloshinskii-Moriya interaction
• Laughlin topology on fractal lattices without area law entanglement
• An efficient Monte Carlo algorithm for the evaluation of Renyi entanglement entropy of a general quantum dimer model at the R-K point
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Topological entanglement entropy in Gutzwiller projected spin liquids
• Classification of trivial spin-1 tensor network states on a square lattice
• Mutual information and correlations across topological phase transitions in topologically ordered graphene zigzag nanoribbons
• Irreducible many-body correlations in topologically ordered systems
• Spin liquid mediated RKKY interaction
• Stability of topological purity under random local unitaries
• Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point
• Generalized toric codes on twisted tori for quantum error correction
• Dynamics and Quantum correlations in Two independently driven Rydberg atoms with distinct laser fields
• On Quantum Entanglement in Topological Phases on a Torus
• Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model
• Measuring topological entanglement entropy using Maxwell relations
• Theory of quantum kagome ice and vison zero modes
• Vanishing k-space fidelity and phase diagram's bulk-edge-bulk correspondence
• Role of conservation laws in the Density Matrix Renormalization Group
• A continuous family of fully-frustrated Heisenberg model on the Kagome lattice
• An entropic invariant for 2D gapped quantum phases
• Schwinger boson study of the $J_1$-$J_2$-$J_3$ kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Distinct-symmetry spin liquid states and phase diagram of Kitaev-Hubbard model
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Bulk Entanglement Spectrum in Gapped Spin Ladders
• Strain tuning of highly frustrated magnets: Order and disorder in the distorted kagome Heisenberg antiferromagnet
• Ground Subspaces of Topological Phases of Matter as Error Correcting Codes
• Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice
• Emergent gauge dynamics of highly frustrated magnets
• Effects of Dzyaloshinskii-Moriya interactions in volborthite: Magnetic orders and thermal Hall effect
• Room temperature relaxometry of single nitrogen-vacancy centers in proximity to $\alpha$-RuCl${}_3$ nanoflakes
• Thermal state entanglement entropy on a quantum graph
• Quantum spin liquid from electron-phonon coupling
• Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets
• Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
• Spin-tensor Meissner currents of ultracold bosonic gas in an optical lattice
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• New disordered anyon phase of doped graphene zigzag nanoribbon
• Thermodynamic, dynamic and transport properties of quantum spin liquid in herbertsmithite from experimental and theoretical point of view
• Finite size effects in the Z_2 spin liquid on the kagome lattice
• Spin-momentum entanglement in a Bose-Einstein condensate
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Chiral spin liquid in a ${\mathbb{Z}}_3$ Kitaev model
• Synthetic Hall tube of interacting fermions
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems
• Entanglement transition through Hilbert-space localization
• Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Capturing magic angles in twisted bilayer graphene from information theory markers
• Novel quantum phases on graphs using abelian gauge theory
• Distilling momentum-space entanglement in Luttinger liquids at finite temperature
• Characterization of helical states in semiconductor quantum wells using quantum information quantities
• Continuous Wigner-Mott transition at $\nu =1/5$
• Behavior under magnetic field of resonance at the edge of the upper Hubbard band in 1T-TaS2
• Signatures of gapless fermionic spinons on a strip of the kagome Heisenberg antiferromagnet
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Simulating spin systems with Majorana networks
• Universal Renyi mutual information in classical systems: the case of kagome ice
• Entanglement detection in quantum materials with competing orders
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Crystalline invariants of fractional Chern insulators
• Partially disordered Heisenberg antiferromagnet with short-range stripe correlations
• Confinement and oscillating deconfinement crossover of two-magnon excitations in quantum spin chains quantified by spin entanglement entropy
• Quantum dissection of a covalent bond with the entanglement spectrum
• Anomalous fractional quantization in the kagomelike Heisenberg ladder: Emergence of the effective spin-1 chain
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Thermal Hall response of an abelian chiral spin liquid at finite temperatures
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Entanglement flow in the Kane-Fisher quantum impurity problem
• Strong relevance of Zinc impurity in the spin-$\frac{1}{2}$ Kagome quantum antiferromagnets: a variational study
• Building Entanglement Entropy out of Correlation Functions for Interacting Fermions
• Topological characterization of magnon-polaron bands and thermal Hall conductivity in a frustrated kagome antiferromagnet
• Topological Phase Transitions in a Constrained Two-Qubit Quantum Control Landscape
• Inverse Hamiltonian design of highly-entangled quantum systems
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Amplifying quantum correlations with quench dynamics in a quantum spin chain: Steady-states versus ground-states
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group
• Condensation Completion and Defects in 2+1D Topological Orders
• Topical review: the nature of the ground state and possibility of a quantum spin liquid in 1T metal dichalcogenides
• Entanglement distance between quantum states and its implications for density-matrix-renormalization-group study of degenerate ground-states
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Self-consistent spin-wave analysis of the 1/3 magnetization plateau in the kagome antiferromagnet
• Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model
• Energy gap of neutral excitations implies vanishing charge susceptibility
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Quantifying the Phase Diagram and Hamiltonian of $S=1/2$ Kagome Antiferromagnets: Bridging Theory and Experiment
• Entanglement Entropy and Quantum Phase Transition in the $O(N)$ $\sigma$-model
• Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Variational methods for characterizing matrix product operator symmetries
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• Instantons and topological order in two-leg electron ladders: A universality class
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas
• Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry
• Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation
• Partons from stabilizer codes
• Multipartite entanglement in quantum phase transitions
• Anomalies of kagome antiferromagnets on magnetization plateaus
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Entanglement entropy as a probe of topological phase transitions
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• The behavior of the entanglement entropy in interacting quasi-1D systems and its consequences for their efficient numerical study
• Tensor network states for the description of quantum many-body systems
• Ground state of the staggered Heisenberg-$\Gamma$ honeycomb model in a magnetic field
• Melting a Rydberg ice to a topological spin liquid with cavity vacuum fluctuation
• Ground state many-body quantum entanglement of frustrated transverse field models on square lattice
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Probing non-Gaussian correlations through entanglement generation in a many-body quantum system