Complete classification of 1D gapped quantum phases in interacting spin systems

Abstract

Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D spin systems in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B \textbf{83}, 035107 (2011); arXiv:1008.3745]. It was found that, such symmetry protected topological (SPT) phases are labeled by the projective representations of the symmetry group which can be viewed as a symmetry fractionalization. In this paper, we extend the classification of 1D gapped phases by considering SPT phases with combined time reversal, parity, and/or on-site unitary symmetries and also the possibility of symmetry breaking. We clarify how symmetry fractionalizes with combined symmetries and also how symmetry fractionalization coexists with symmetry breaking. In this way, we obtain a complete classification of gapped quantum phases in 1D spin systems. We find that in general, symmetry fractionalization, symmetry breaking and long range entanglement(present in 2 or higher dimensions) represent three main mechanisms to generate a very rich set of gapped quantum phases. As an application of our classification, we study the possible SPT phases in 1D fermionic systems, which can be mapped to spin systems by Jordan-Wigner transformation.

15 pages, 3 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Matrix product states represent ground states faithfully
• Entropy scaling and simulability by Matrix Product States
• String order and symmetries in quantum spin lattices
• Doped Kagome System as Exotic Superconductor
• Mutual Chern-Simons theory for Z_2 topological order

Cited by in corpus (344)

• Classification of topological quantum matter with symmetries
• Quantum Spin Liquid States
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Braiding statistics approach to symmetry-protected topological phases
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Interacting topological insulators: a review
• Detection of Symmetry Protected Topological Phases in 1D
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Topological phases with parafermions: theory and blueprints
• Random-matrix theory of Majorana fermions and topological superconductors
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Braiding statistics of loop excitations in three dimensions
• On the classification of topological orders
• Gauging spatial symmetries and the classification of topological crystalline phases
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Intrinsically Gapless Topological Phases
• Experimental characterization of fragile topology in an acoustic metamaterial
• Gapless Symmetry Protected Topological Order
• Gauging quantum states: from global to local symmetries in many-body systems
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• Measurement as a shortcut to long-range entangled quantum matter
• Wire deconstructionism of two-dimensional topological phases
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Abelian Floquet symmetry-protected topological phases in one dimension
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Symmetry constraints on many-body localization
• Symmetry Protected Topological phases and Generalized Cohomology
• Long-range entanglement from measuring symmetry-protected topological phases
• Topological invariants for gauge theories and symmetry-protected topological phases
• Entanglement rates and area laws
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Characterization of a topological Mott insulator in one dimension
• Classification of subsystem symmetry-protected topological phases
• Topological Luttinger Liquids from Decorated Domain Walls
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Computational Power of Symmetry-Protected Topological Phases
• Lecture Notes on Generalized Symmetries and Applications
• The 1D Ising model and topological order in the Kitaev chain
• Many-body localization, symmetry, and topology
• Topology of one dimensional quantum systems out of equilibrium
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Topological order in 1D Cluster state protected by symmetry
• Faster identification of optimal contraction sequences for tensor networks
• On lattice models of gapped phases with fusion category symmetries
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Topological charge pumping in the interacting bosonic Rice-Mele model
• On topological phases of spin chains
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Universal quantum computation using fractal symmetry-protected cluster phases
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
• Symmetry protected topological order at nonzero temperature
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Quantum circuit complexity of one-dimensional topological phases
• Short-range entanglement and invertible field theories
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Classification of topological phases with finite internal symmetries in all dimensions
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Interaction effects on 1D fermionic symmetry protected topological phases
• Almost all multipartite qubit quantum states have trivial stabilizer
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Topological phases in gapped edges of fractionalized systems
• Mixed-state long-range order and criticality from measurement and feedback
• Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Area law of non-critical ground states in 1D long-range interacting systems
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Minimalist approach to the classification of symmetry protected topological phases
• Characterizing Topological Order with Matrix Product Operators
• Dynamical engineering of interactions in qudit ensembles
• Distinct trivial phases protected by a point-group symmetry in quantum spin chains
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• From symmetry-protected topological order to Landau order
• Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Topological and symmetry-enriched random quantum critical points
• Fermionized parafermions and symmetry-enriched Majorana modes
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
• Symmetry-protected self-correcting quantum memories
• Classifying phases protected by matrix product operator symmetries using matrix product states
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
• Unraveling of the fractional topological phase in one-dimensional flatbands with nontrivial topology
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Loop braiding statistics in exactly soluble 3D lattice models
• Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks
• String-Net Models with $Z_N$ Fusion Algebra
• Parity quantum numbers in the Density Matrix Renormalization Group
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Classification of Matrix-Product Unitaries with Symmetries
• Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles
• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Symmetry-protected topologically ordered states for universal quantum computation
• A universal formula for the entanglement asymmetry of matrix product states
• Entanglement entropy of (3+1)D topological orders with excitations
• Spin Topological Field Theory and Fermionic Matrix Product States
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Searching for Fracton Orders via Symmetry Defect Condensation
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Local characterization of 1d topologically ordered states
• Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Classifying local fractal subsystem symmetry protected topological phases
• Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems
• Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Lattice model constructions for gapless domain walls between topological phases
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Classification of Mixed State Topology in One Dimension
• Quantum spin systems for measurement-based quantum computation
• Symmetry protected entanglement renormalization
• Symmetry-Protected Topological Entanglement
• Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries $G_f$ and in any dimensions
• Interaction Enabled Topological Crystalline Phases
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
• Anyonic Haldane insulator in one dimension
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
• Constraints on order and disorder parameters in quantum spin chains
• Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Observing Floquet topological order by symmetry resolution
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid
• On the stability of charges in infinite quantum spin systems
• Unwinding Short-Range Entanglement
• Fate of exceptional points under interactions: Reduction of topological classifications
• Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Quantum phase transition and critical behavior between the gapless topological phases
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Bosonic Crystalline Symmetry Protected Topological Phases Beyond the Group Cohomology Proposal
• Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
• Symmetry Protected Quantum State Renormalization
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• Folding approach to topological orders enriched by mirror symmetry
• Topological Field Theory and Matrix Product States
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Symmetry-Enriched Criticality in a Coupled Spin-Ladder
• Brane parity orders in the insulating state of Hubbard ladders
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Stability of the Area Law for the Entropy of Entanglement
• Scaling of geometric phase versus band structure in cluster-Ising models
• Heisenberg antiferromagnet on the Husimi lattice
• Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders
• Symmetry-protected topological order in magnetization plateau states of quantum spin chains
• Product vacua with boundary states and the classification of gapped phases
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Multiversality and Unnecessary Criticality in One Dimension
• Tensor network representations from the geometry of entangled states
• Matrix product states for topological phases with parafermions
• Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• An infinite family of 3d Floquet topological paramagnets
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Matrix Product States: Entanglement, symmetries, and state transformations
• Surface field theories of point group symmetry protected topological phases
• All spin-1 topological phases in a single spin-2 chain
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Irreducible Projective Representations and Their Physical Applications
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Effective field theories of topological crystalline insulators and topological crystals
• Holographic Geometries of one-dimensional gapped quantum systems from Tensor Network States
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• Geometry of reduced density matrices for symmetry-protected topological phases
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain
• Symmetry-protected topological phase in a one-dimensional correlated bosonic model with a synthetic spin-orbit coupling
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Bosonization for fermions and parafermions
• Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction
• Non universality of entanglement convertibility
• Entanglement properties of the Haldane phases: A finite system-size approach
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Fractalizing quantum codes
• Hidden Magnetism in Periodically Modulated One Dimensional Dipolar Fermions
• Symmetry protected phases in inhomogeneous spin chains
• Holographic spin networks from tensor network states
• Quantum Current and Holographic Categorical Symmetry
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Disentangling transitions in topological order induced by boundary decoherence
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Entanglement properties of spin models in triangular lattices
• Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
• Signatures of broken parity and time-reversal symmetry in generalized string-net models
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Quantum phase transitions of topological insulators without gap closing
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Control of superexchange interactions with DC electric fields
• Plateau transitions of spin pump and bulk-edge correspondence
• Comparative study of the density matrix embedding theory for the Hubbard models
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Detecting topological transitions in two dimensions by Hamiltonian evolution
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Topological degeneracy (Majorana zero-mode) and 1+1D fermionic topological order in a magnetic chain on superconductor via spontaneous Z2 symmetry breaking
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Quantum Error-Detection at Low Energies
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Superuniversality from disorder at two-dimensional topological phase transitions
• Category of SET orders
• Supersymmetric boundaries of one-dimensional phases of fermions beyond symmetry-protected topological states
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Generalized toric codes on twisted tori for quantum error correction
• Dimerization, Trimerization and Quantum pumping
• Classical origins of Landau-incompatible transitions
• Introduction to quantum entanglement in many-body systems
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Symmetry-protected intermediate trivial phases in quantum spin chains
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Classical topological paramagnetism
• Exactly solvable lattice models for interacting electronic insulators in two dimensions
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Topological phase transition and the effect of Hubbard interaction on the one-dimensional topological Kondo insulator
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Error-correction properties of an interacting topological insulator
• Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers
• Composite symmetry protected topological order and effective models
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Infinite-size density matrix renormalization group with parallel Hida's algorithm
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• State Space Geometry of the Spin-1 Antiferromagnetic Heisenberg Chain
• Symmetry protected topological phases in spin-1 ladders and their phase transitions
• Area laws and efficient descriptions of quantum many-body states
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Duality and Stacking of Bosonic and Fermionic SPT Phases
• Fractionalized time reversal, parity and charge conjugation symmetry in topological superconductor: a possible origin of three generations of neutrinos and mass mixing
• Symmetry-protected topological phase transitions and robust chiral order on a tunable zigzag lattice
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Composite Quantum Phases in Non-Hermitian Systems
• Classifying parafermionic gapped phases using matrix product states
• Symmetry-protected trivial phases and quantum phase transitions in an anisotropic antiferromagnetic spin-1 biquadratic model
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Realization of the topological Hopf term in two-dimensional lattice models
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Quasi-fractionalization of spin in a cluster-based Haldane state supported by chirality of a triangular spin tube
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Complete characterization of spin chains with two Ising symmetries
• Symmetries and local transformations of translationally invariant Matrix Product States
• Fractional domain wall statistics in spin chains with anomalous symmetries
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Internal structure of gauge-invariant Projected Entangled Pair States
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• A Classifying Space for Phases of Matrix Product States
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Quantum Restored Symmetry Protected Topological Phases
• One-dimensional symmetric phases protected by frieze symmetries
• Eleven Competing Phases in the Heisenberg-Gamma (J$\Gamma$) Ladder
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Instanton effects in lattice models of bosonic symmetry-protected topological states
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Threefold Way for Typical Entanglement
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Model-Independent Quantum Phases Classifier
• Topological phases of the compass ladder model
• Holographic duality between bulk topological order and boundary mixed-state order
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
• On ground state phases of quantum spin systems
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly
• Construction of Entangled Many-body States via the Higgs Mechanism
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
• Universal entanglement correction induced by relevant deformations at the quantum critical point
• Spurious Strange Correlators in Symmetry-Protected Topological Phases
• Topological phases of bosons with local parity coupling on a dimerized lattice
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States