Topological Phases of One-Dimensional Fermions: An Entanglement Point of View

Abstract

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by Fidkowski \emph{et. al.} (Phys. Rev. B 81, 134509 (2010)), we find that in the presence of interactions there are only eight distinct phases, which obey a ${\mathbb{Z}}_8$ group structure. This is in contrast to the $\mathbb{Z}$ classification in the non-interacting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.

12 pages, 1 figure; journal ref. added

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological phases of fermions in one dimension
• The iTEBD algorithm beyond unitary evolution
• String order and symmetries in quantum spin lattices
• Rise and fall of hidden string order of lattice bosons
• Holographic quantum states
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter

Cited by in corpus (409)

• Classification of topological quantum matter with symmetries
• Towards a derivation of holographic entanglement entropy
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological phases of fermions in one dimension
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Learning phase transitions by confusion
• Quantum entanglement in condensed matter systems
• Symmetry Protected Topological phases of Quantum Matter
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Gravitation from Entanglement in Holographic CFTs
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Interacting topological insulators: a review
• Relative Entropy and Holography
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• A classification of symmetry enriched topological phases with exactly solvable models
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological phases with parafermions: theory and blueprints
• Random-matrix theory of Majorana fermions and topological superconductors
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Topological classification with additional symmetries from Clifford algebras
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Classification of interacting electronic topological insulators in three dimensions
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Classification of Interacting Topological Floquet Phases in One Dimension
• Symmetry protected topological phases from decorated domain walls
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Many-body Localization and Symmetry Protected Topological Order
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Interacting topological phases and modular invariance
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Reflection positivity and invertible topological phases
• Subsystem symmetry protected topological order
• Topological phases protected by point group symmetry
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Colloquium: Atomic spin chains on surfaces
• Building crystalline topological phases from lower-dimensional states
• Theory of defects in Abelian topological states
• Bulk-Edge Correspondence in the Entanglement Spectra
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Majorana states in helical Shiba chains and ladders
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Interaction effect on topological classification of superconductors in two dimensions
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Gapless topological phases and symmetry-enriched quantum criticality
• Manipulating Topological Edge Spins in One-Dimensional Optical Lattice
• Topology and edge modes in quantum critical chains
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Topological invariants and interacting one-dimensional fermionic systems
• The half-filled Landau level: the case for Dirac composite fermions
• 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
• Wire deconstructionism of two-dimensional topological phases
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Exact Matrix Product States for Quantum Hall Wave Functions
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Average Symmetry-Protected Topological Phases
• Symmetry constraints on many-body localization
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Long-range entanglement from measuring symmetry-protected topological phases
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Fractal Symmetric Phases of Matter
• Majorana Edge States in Interacting Two-chain Ladders of Fermions
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Axion topological field theory of topological superconductors
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Characterization of a topological Mott insulator in one dimension
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Topological fractional pumping with alkaline-earth(-like) ultracold atoms
• Majorana edge states in two atomic wires coupled by pair-hopping
• Tunneling spectra simulation of interacting Majorana wires
• Higher-order Topological Mott Insulators
• Topological Phase Transition without Gap Closing
• Localized Majorana-like modes in a number conserving setting: An exactly solvable model
• Topological Luttinger Liquids from Decorated Domain Walls
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions
• Symmetry resolved entanglement: Exact results in 1D and beyond
• Many-body localization, symmetry, and topology
• Topology of one dimensional quantum systems out of equilibrium
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Non-Abelian topological insulators from an array of quantum wires
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Long-range topological insulators and weakened bulk-boundary correspondence
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Topological charge pumping in the interacting bosonic Rice-Mele model
• On topological phases of spin chains
• Symmetric Mass Generation
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• A study on correlation effects in two dimensional topological insulators
• Twist operators in higher dimensions
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Time-reversal symmetric U(1) quantum spin liquids
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Topological states in a microscopic model of interacting fermions
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Particle-hole symmetry, many-body localization, and topological edge modes
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Topological phase in one-dimensional interacting fermion system
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Quantum circuit complexity of one-dimensional topological phases
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Chiral central charge from a single bulk wave function
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Flux insertion, entanglement, and quantized responses
• Interaction effects on 1D fermionic symmetry protected topological phases
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Microscopic model for the boson integer quantum Hall effect
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Topological phases in gapped edges of fractionalized systems
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Entanglement topological invariants for one-dimensional topological superconductors
• Symmetry protected topological phases under decoherence
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Electrically Tunable Conductance and Edge Modes in Topological Crystalline Insulator Thin Films: Tight-Binding Model Analysis
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Non-Hermitian Mott Skin Effect
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Gauging the Kitaev chain
• The Thouless theorem for matrix product states and subsequent post-density matrix renormalization group methods
• Exceptional band touching for strongly correlated systems in equilibrium
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Quenched dynamics and spin-charge separation in an interacting topological lattice
• Bosonic integer quantum Hall effect in optical flux lattices
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• From symmetry-protected topological order to Landau order
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• CPT theorem and classification of topological insulators and superconductors
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Parafermionic phases with symmetry-breaking and topological order
• Exact zero modes in twisted Kitaev chains
• Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Topological and symmetry-enriched random quantum critical points
• Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI
• Z4 parafermions in one-dimensional fermionic lattices
• Symmetry Protected Topological Charge in Symmetry Broken Phase: Spin-Chern, Spin-Valley-Chern and Mirror-Chern Numbers
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Many-body Majorana operators and the equivalence of parity sectors
• Fermionized parafermions and symmetry-enriched Majorana modes
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• A proposal to probe quantum non-locality of Majorana fermions in tunneling experiments
• Topological phases of parafermions: a model with exactly-solvable ground states
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Universal entanglement spectrum in gapless symmetry protected topological states
• Topological invariant for generic 1D time reversal symmetric superconductors in class DIII
• The Topological Relation Between Bulk Gap Nodes and Surface Bound States : Application to Iron-based Superconductors
• The interacting Rice-Mele model: bulk and boundaries
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Construction of Hamiltonians by supervised learning of energy and entanglement spectra
• Topological Insulators and Quantum Spin Liquids
• Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Topological superconductivity and Majorana states in low-dimensional systems
• Lieb-Schultz-Mattis theorems for symmetry protected topological phases
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model
• Pretopological fractional excitations in the two-leg flux ladder
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• On gapped phases with a continuous symmetry and boundary operators
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Classifying Quantum Phases With The Torus Trick
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Disorder Protected and Induced Local Zero-Modes in Longer-Range Kitaev Chains
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Interaction Enabled Topological Crystalline Phases
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
• Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• Dimensional hierarchy of fermionic interacting topological phases
• Surface codes, quantum circuits, and entanglement phases
• Polarization and entanglement spectrum in non-hermitian systems
• Majorana Quasi-Particles Protected by ${\mathbb{Z}}_2$ Angular Momentum Conservation
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Edge insulating topological phases in a two-dimensional long-range superconductor
• Signatures of topology in quantum quench dynamics and their interrelation
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Topological Pair-Density-Wave Superconducting States
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
• Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• First-Order Topological Quantum Phase Transition in a Strongly Correlated Ladder
• Magnetic states in a three-dimensional topological Kondo insulator
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Fate of exceptional points under interactions: Reduction of topological classifications
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• String flux mechanism for fractionalization in topologically ordered phases
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Supersolid-Superfluid phase separation in the extended Bose-Hubbard model
• Phase Diagram and Entanglement of two interacting topological Kitaev chains
• Luttinger liquid in contact with a Kramers pair of Majorana bound states
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Symmetry Protected Quantum State Renormalization
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors
• Homotopical Foundations of Parametrized Quantum Spin Systems
• Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation
• Brane parity orders in the insulating state of Hubbard ladders
• Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Bosonic symmetry protected topological phases with reflection symmetry
• Visualizing Quasiparticles from Quantum Entanglement for general 1D phases
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Interaction-enabled topological phases in topological insulator-superconductor heterostructures
• Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly-interacting to the non-interacting limit
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Emergence of spontaneous symmetry breaking in dissipative lattice systems
• ${\mathbb{Z}}_3$ parafermionic zero modes without Andreev backscattering from the $2/3$ fractional quantum Hall state
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Entanglement in a second order topological insulator on a square lattice
• Rational indices for quantum ground state sectors
• Topological protection of Majorana polaritons in a cavity
• Changing anyonic ground degeneracy with engineered gauge fields
• An infinite family of 3d Floquet topological paramagnets
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Surface field theories of point group symmetry protected topological phases
• Chern-Simons superconductors and their instabilities
• Out of Equilibrium Majoranas in Interacting Kitaev Chains
• Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
• Quench Dynamics of Topological Maximally-Entangled States
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Effective field theories of topological crystalline insulators and topological crystals
• Majorana zero modes and their bosonization
• Characterization of a correlated topological Kondo insulator in one dimension
• 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
• Topological d-wave superconductivity in two dimensions
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Topological Devil's staircase in atomic two-leg ladders
• Finite Size Scaling of Topological Entanglement Entropy
• Bosonization for fermions and parafermions
• Detecting phase boundaries of quantum spin-1/2 XXZ ladder via bipartite and multipartite entanglement transitions
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Definition and Classification of Fermi Surface Anomalies
• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
• Symmetry protected phases in inhomogeneous spin chains
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Dyonic zero-energy modes
• Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Homogeneous and domain wall topological Haldane conductors with dressed Rydberg atoms
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Renormalization group approach to symmetry protected topological phases
• Quantum phase transitions of topological insulators without gap closing
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Topological phases of parafermionic chains with symmetries
• Quantum phases of a one-dimensional Majorana-Bose-Hubbard model
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• From edge to bulk: Cavity induced displacement of topological non-local qubits
• Majorana end states in an interacting quantum wire
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Comparative study of the density matrix embedding theory for the Hubbard models
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Topologically enabled superconductivity
• Superuniversality from disorder at two-dimensional topological phase transitions
• A many-body Fredholm index for ground state spaces and Abelian anyons
• Gapping fragile topological bands by interactions
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Entropic topological invariant for a gapped one-dimensional system
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Transport properties of an interacting Majorana chain
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• 4D beyond-cohomology topological phase protected by $C_2$ symmetry and its boundary theories
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Practical new platform for interaction-enabled topological phases
• Entanglement in non-critical inhomogeneous quantum chains
• Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
• Interaction quench and thermalization in a one-dimensional topological Kondo insulator
• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Theory of quantum kagome ice and vison zero modes
• Geometric Approach to 3D Interfaces at Strong Coupling
• Entanglement gap, corners, and symmetry breaking
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Majorana edge-modes in a spinful particle conserving model
• Topological phase transition and the effect of Hubbard interaction on the one-dimensional topological Kondo insulator
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• Area laws and efficient descriptions of quantum many-body states
• Topological physics in quantum critical systems
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Synthetic Hall tube of interacting fermions
• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Multi-hole models for deterministically placed acceptor arrays in silicon
• Interactions and the Theta Term in One-Dimensional Gapped Systems
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• The global phase diagram of the cluster-XY spin chain with dissipation
• Two-dimensional Paired Topological Superfluids of Rydberg Fermi Gases
• Classifying parafermionic gapped phases using matrix product states
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Unwinding of a one-dimensional topological superconductor
• Interacting Chern Insulator in Infinite Spatial Dimensions
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Gauging Defects in Quantum Spin Systems
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Quantum Entanglement Dynamics of Spacetime and Matter
• Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Relaxation of the entanglement spectrum in quench dynamics of topological systems
• A geometrical crossover in excited states of two-electron quantum dots in a magnetic field
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Complete characterization of spin chains with two Ising symmetries
• Many Body Density of States of a system of non interacting spinless fermions
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Observability of a Sharp Majorana Transition in a Few-Body Model
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Quantum Restored Symmetry Protected Topological Phases
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Topological Dipole Insulator
• 1D Error Correcting Code for Majorana Qubits
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Entanglement gap in 1D long-range quantum spherical models
• Topological phases protected by projective space-time inversion symmetry in alkaline-earth-metal-like atoms
• Quantum Degenerate Majorana Surface Zero Modes in Two-Dimensional Space
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• First Order Topological Phase Transitions and Disorder Induced Majorana Modes in Interacting Fermion Chains
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination
• Entanglement signatures of a percolating quantum system
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition
• Entanglement entropy as a probe of topological phase transitions
• Symmetry-protected topological wire in a topological vacuum