The effects of interactions on the topological classification of free fermion systems

Abstract

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification is an integer, but with the introduction of interactions it becomes well defined only modulo 8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct free phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field theory interpretation of this phenomenon. There is a second order phase transition between the two phases in the free theory which can be avoided by going through the strongly interacting region. We show that this transition is in the 2D Ising universality class, where a first order phase transition line, terminating at a second order transition, can be avoided by going through the analogue of a high temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e. the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first order Peierls transition region, a second order transition region, and a region with no transition.

9 pages, 5 figures. v3: reference added, bibliography cleaned up

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• 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
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect

Cited by in corpus (446)

• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Topological Superconductivity in Twisted Multilayer Graphene
• Fermion Path Integrals And Topological Phases
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Majorana Fermions and Topology in Superconductors
• Single particle Green's functions and interacting topological insulators
• 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
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Topological phases with parafermions: theory and blueprints
• Interacting fermionic topological insulators/superconductors in three dimensions
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Pre-thermal phases of matter protected by time-translation symmetry
• Topological classification with additional symmetries from Clifford algebras
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological Superconductivity in a Planar Josephson Junction
• Equilibration and Order in Quantum Floquet Matter
• Majorana edge states in interacting one-dimensional systems
• Twisted equivariant matter
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Classification of topological phases in periodically driven interacting systems
• Simplified topological invariants for interacting insulators
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Interacting topological phases and modular invariance
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Reflection positivity and invertible topological phases
• Topological Order Parameters for Interacting Topological Insulators
• Majorana zero modes in a quantum Ising chain with longer-ranged interactions
• Subsystem symmetry protected topological order
• Topological surface states in nodal superconductors
• Choreographed entangle dances: topological states of quantum matter
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Gauging spatial symmetries and the classification of topological crystalline phases
• Fractional topological superconductors with fractionalized Majorana fermions
• 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
• Topology and edge modes in quantum critical chains
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Manipulating Topological Edge Spins in One-Dimensional Optical Lattice
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Gapless Symmetry Protected Topological Order
• Topological invariants and interacting one-dimensional fermionic systems
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• The half-filled Landau level: the case for Dirac composite fermions
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• Wire deconstructionism of two-dimensional topological phases
• Topological field theory and thermal responses of interacting topological superconductors
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Abelian Floquet symmetry-protected topological phases in one dimension
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Phase Diagram of the Interacting Majorana Chain Model
• Many-body topology of non-Hermitian systems
• Majorana nanowires for topological quantum computation
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• 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
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Characterization of a topological Mott insulator in one dimension
• Majorana Fermion Codes
• Topological fractional pumping with alkaline-earth(-like) ultracold atoms
• Topological Hamiltonian as an Exact Tool for Topological Invariants
• Interacting topological phases in multiband nanowires
• Higher-order Topological Mott Insulators
• Topological Phase Transition without Gap Closing
• Topological Luttinger Liquids from Decorated Domain Walls
• Superconductivity and Local Inversion-Symmetry Breaking
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Topological invariants for interacting topological insulators with inversion symmetry
• Many-body localization, symmetry, and topology
• Symmetric Fracton Matter: Twisted and Enriched
• Strongly interacting Majorana fermions
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Braiding Majorana corner modes in a second-order topological superconductor
• Crystalline topological phases as defect networks
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Nonlinearity induced topological physics in momentum space and real space
• Global Anomalies on the Hilbert Space
• Exotic Quantum Phase Transitions of $(2+1)d$ Dirac fermions
• On topological phases of spin chains
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Symmetric Mass Generation
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• A study on correlation effects in two dimensional topological insulators
• Topological carbon materials: a new perspective
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Particle-hole symmetry, many-body localization, and topological edge modes
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Composite Dirac liquids: parent states for symmetric surface topological order
• Anomalies and Symmetry Fractionalization
• Topological phase in one-dimensional interacting fermion system
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Classification of topological phases with finite internal symmetries in all dimensions
• Flux insertion, entanglement, and quantized responses
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Dai-Freed theorem and topological phases of matter
• Interaction effects on 1D fermionic symmetry protected topological phases
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Comments on Symmetric Mass Generation in 2d and 4d
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Effective field theories for topological insulators by functional bosonization
• Symmetry protected topological phases under decoherence
• Fermion mass without symmetry breaking
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Topological Varma superfluid in optical lattices
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Proximity induced superconductivity in Weyl semi-metals
• Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation
• Real-space recipes for general topological crystalline states
• Symmetry Breaking in Coupled SYK or Tensor Models
• Non-Hermitian Mott Skin Effect
• Composite fermion duality for half-filled multicomponent Landau Levels
• Exceptional band touching for strongly correlated systems in equilibrium
• Andreev reflection from a topological superconductor with chiral symmetry
• Anomalous Symmetries End at the Boundary
• Fragile topological phases in interacting systems
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Stabilizing multiple topological fermions on a quantum computer
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• CPT theorem and classification of topological insulators and superconductors
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Magnetic Order Driven Topological Transition in the Haldane-Hubbard Model
• $SL(2,\mathbb{Z})$ action on QFTs with ${\mathbb{Z}}_2$ symmetry and the Brown-Kervaire invariants
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Exact zero modes in twisted Kitaev chains
• Gapped Chiral Fermions
• Fermionized parafermions and symmetry-enriched Majorana modes
• Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI
• Many-body Majorana operators and the equivalence of parity sectors
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Topological Superconductors on Superstring Worldsheets
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Weak symmetry breaking in two dimensional topological insulators
• All-fermion electrodynamics and fermion number anomaly inflow
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Reentrant topological transitions in a quantum wire/superconductor system with quasiperiodic lattice modulation
• Loop braiding statistics in exactly soluble 3D lattice models
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• A gauge theory generalization of the fermion-doubling theorem
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• The interacting Rice-Mele model: bulk and boundaries
• Fermion masses through four-fermion condensates
• Symmetry Protected Topological Phases in Spin Ladders with Two-body Interactions
• The fate and heir of Majorana zero modes in a quantum wire array
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Novel phases in strongly coupled four-fermion theories
• Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Quantum phase transitions in Dirac fermion systems
• Andreev-Majorana bound states in superfluids
• Topological superconductivity and Majorana states in low-dimensional systems
• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Theory of a quantum spin liquid in hydrogen-intercalated honeycomb iridate, H3LiIr2O6
• Topological Insulators and Quantum Spin Liquids
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Fermion masses without symmetry breaking in two spacetime dimensions
• Non-Hermitian many-body topological excitations in interacting quantum dots
• Bridging Fermionic and Bosonic Short Range Entangled States
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Topological Insulators and Superconductors from String Theory
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Nonlinear Dirac Cones
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Dimensional crossover and cold-atom realization of topological Mott insulators
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Multiband s-wave topological superconductors: role of dimensionality and magnetic field response
• Determining topological order from a local ground state correlation function
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• The algebra of anomaly interplay
• The Origin of Families and $SO(18)$ Grand Unification
• $SO(4)$ invariant Higgs-Yukawa model with reduced staggered fermions
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
• GSO projections via SPT phases
• Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Correlation effects on topological crystalline insulators
• Global alignment of solution-based single-wall carbon nanotube films via machine-vision controlled filtration
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
• Interaction Enabled Topological Crystalline Phases
• Dimensional hierarchy of fermionic interacting topological phases
• Study of the phase diagram of the Kitaev-Hubbard chain
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Fermionic quantum cellular automata and generalized matrix product unitaries
• The classification of symmetry protected topological phases of one-dimensional fermion systems
• Holographic fractional topological insulators in 2+1 and 1+1 dimensions
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
• Topological Pair-Density-Wave Superconducting States
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Magnetic states in a three-dimensional topological Kondo insulator
• Non-Hermitian Topology in Hermitian Topological Matter
• Unwinding Short-Range Entanglement
• Chiral Lattice Fermions From Staggered Fields
• Fate of exceptional points under interactions: Reduction of topological classifications
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Ultra Unification
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion
• Fermions with cubic and quartic spectrum
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• The Mott transition as a topological phase transition
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Information Scrambling with Conservation Laws
• (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions
• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• $\text{Draiding}$ majoranas to dynamically engineer Hamiltonians
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Doubled Shapiro Steps in a Topological Josephson Junction
• Luttinger liquid in contact with a Kramers pair of Majorana bound states
• Phase Diagram and Entanglement of two interacting topological Kitaev chains
• Topological edge Mott insulating state in two dimensions at finite temperatures -bulk and edge analysis-
• Topological Superfluid and Majorana Zero Modes in Synthetic Dimension
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Topology and strong four fermion interactions in four dimensions
• 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
• Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Fermi Surface Symmetric Mass Generation
• Interaction-enabled topological phases in topological insulator-superconductor heterostructures
• What Symmetries are Preserved by a Fermion Boundary State?
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly-interacting to the non-interacting limit
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Partition Functions and Stability Criteria of Topological Insulators
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Topological and quantum critical properties of the interacting Majorana chain model
• Topological $s$-wave superconductors driven by electron correlation
• 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
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Topological protection of Majorana polaritons in a cavity
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Stability of Topological character of Weyl Semi-metal, and Topological Dipole in Holography
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
• Instability and topological robustness of Weyl semimetals against Coulomb interaction
• Majorana zero modes and their bosonization
• Quench Dynamics of Topological Maximally-Entangled States
• An Operational Definition of Topological Order
• Translation invariant topological superconductors on lattice
• Topological d-wave superconductivity in two dimensions
• Topological Defects in Floquet Circuits
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• One-dimensional non-interacting topological insulators with chiral symmetry
• Hard-core bosons in one-dimensional interacting topological bands
• Interacting topological mirror excitonic insulator in one dimension
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Evolution of edge states in topological superfluids during the quantum phase transition
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Exact Solution to Haldane-BCS-Hubbard Model Along the Symmetric Lines: Interaction Induced Topological Phase Transition
• Definition and Classification of Fermi Surface Anomalies
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Eight-vertex criticality in the interacting Kitaev chain
• Non-abelian bosonization in two and three spatial dimensions and applications
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity
• Gauging anomalous unitary operators
• Stability of the coexistence phase of chiral superconductivity and noncollinear spin ordering with a nontrivial topology and strong electron correlations
• Detecting topology through dynamics in interacting fermionic wires
• Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code
• Interacting Topological Insulators with Synthetic Dimensions
• Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
• Simulating Majorana zero modes on a noisy quantum processor
• Phases of a strongly coupled four-fermion theory
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Topological skyrmion phases of matter
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries
• Topological phases of parafermionic chains with symmetries
• Topological Charge/spin density Wave in InAs/GaSb Quantum Wells under an In-plane Magnetic Field
• Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Gapped Boundary Phases of Topological Insulators via Weak Coupling
• Notes on 8 Majorana Fermions
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Transport properties of an interacting Majorana chain
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• CT or P Problem and Symmetric Gapped Fermion Solution
• Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Symmetry-breaking signatures of multiple Majorana zero modes in one-dimensional spin-triplet superconductors
• Gapping fragile topological bands by interactions
• Theory of topological spin Josephson junctions
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Quantum Monte Carlo simulation of topological phase transitions
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• Practical new platform for interaction-enabled topological phases
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Superconductivity in quantum wires: A symmetry analysis
• Topological phases arising from attractive interaction and pair hopping in the Extended Hubbard Model
• Topological phases in two-legged Heisenberg ladders with alternating interactions
• Dynamical probing of a topological phase of bosons in one dimension
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• Error-correction properties of an interacting topological insulator
• Exactly solvable lattice models for interacting electronic insulators in two dimensions
• Index theorems, generalized Hall currents and topology for gapless defect fermions
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Gauge interactions and topological phases of matter
• Non-local Order Parameters and Quantum Entanglement for Fermionic Topological Field Theories
• LSM and CPT
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Multi-hole models for deterministically placed acceptor arrays in silicon
• Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure
• Critical properties of the Majorana chain with competing interactions
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
• Topological physics in quantum critical systems
• Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordström AdS Black Holes
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Bound states of three fermions forming symmetry-protected topological phases
• Interactions and the Theta Term in One-Dimensional Gapped Systems
• Logical Majorana zero modes in a nanowire network
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Decoding quantum criticalities from fermionic/parafermionic topological states
• Interacting Chern Insulator in Infinite Spatial Dimensions
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Unwinding of a one-dimensional topological superconductor
• The Future of the Correlated Electron Problem
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Emergent Topology in Many-Body Dissipative Quantum Matter
• C-P-T Fractionalization
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Gauging Defects in Quantum Spin Systems
• Dyson's Classification And Real Division Superalgebras
• Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases
• Design of a room-temperature topological exciton-polariton laser in a ZnO/TiO${}_2$-photonic crystal slab
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Polynomial description of inhomogeneous topological superconducting wires
• Stability of the boundary zero modes in one-dimensional topological superconductors
• Complete characterization of spin chains with two Ising symmetries
• Laser assisted tunneling in a Tonks-Girardeau gas
• Topological Superconductivity in Doped Symmetry Protected Topological State
• Fermionic defects of topological phases and logical gates
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Deconfined Quantum Criticality among Grand Unified Theories
• Quantum Restored Symmetry Protected Topological Phases
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Integrability of the $\nu =4/3$ fractional quantum Hall edge states
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Observability of a Sharp Majorana Transition in a Few-Body Model
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Universality classes of order parameters composed of many body bound states
• Inter-species topological phases via a dynamical gauge field
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality
• Quantum Degenerate Majorana Surface Zero Modes in Two-Dimensional Space
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Threefold Way for Typical Entanglement
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Computational Many-Body Physics via ${\mathcal{M}}_{2^q}$ Algebra
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• Supersymmetry in Hadron Spectroscopy and Solitons in 2 Dimensional Fermionic Media
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Correspondence of topological classification between quantum graph extra dimension and topological matter
• Topological order in higher composites
• Entanglement spectrum of gapless topological phases: a case study with topological superconductors
• Reflection-Symmetry Protected Antiferromagnetic Topological Insulator in Three-Dimensional Heavy-Fermion Systems
• Quantum Avalanches in ${\mathbb{Z}}_2$-preserving Interacting Ising Majorana Chain
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
• Topological bound states in a lattice of rings with nearest-neighbour interactions