Symmetry Protected Topological phases of Quantum Matter

Abstract

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no exotic excitations but have non-trivial surface states that are protected by symmetry. We describe the various possible such phases and their properties in three dimensional systems with realistic symmetries. We develop many key ideas of the theory of these states using simple examples. The emphasis is on physical rather than mathematical properties. We survey insights obtained from the study of SPT phases for a number of other theoretical problems.

Invited Review for Annual Reviews of Condensed Matter Physics

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Cited by in corpus (363)

• Classification of topological quantum matter with symmetries
• Topological Bands for Ultracold Atoms
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Floquet Topological Insulators for Sound
• Non-Hermitian topological phenomena: A review
• Interacting topological insulators: a review
• Generalized Symmetries in Condensed Matter
• Three-Dimensional All-Dielectric Photonic Topological Insulator
• Fracton-Elasticity Duality
• Equilibration and Order in Quantum Floquet Matter
• Topology and Broken Symmetry in Floquet Systems
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Dissipative Floquet Topological Systems
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Building crystalline topological phases from lower-dimensional states
• Choreographed entangle dances: topological states of quantum matter
• Dual Dirac liquid on the surface of the electron topological insulator
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Long-range Coulomb interaction in nodal-ring semimetals
• Many-body quantum magic
• Gapless topological phases and symmetry-enriched quantum criticality
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Intrinsically Gapless Topological Phases
• Magnonic topological insulators in antiferromagnets
• Floquet symmetry-protected topological phases in cold atomic systems
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Average Symmetry-Protected Topological Phases
• Duality between $(2+1)d$ Quantum Critical Points
• Emergent Phases of Fractonic Matter
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Disorder in quantum many-body systems
• Floquet topological phases with symmetry in all dimensions
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Classification of subsystem symmetry-protected topological phases
• Many-body topological invariants from randomized measurements
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Topological states from topological crystals
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Topological Luttinger Liquids from Decorated Domain Walls
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Lecture Notes on Generalized Symmetries and Applications
• Disorder Operators and their Descendants
• Symmetric Fracton Matter: Twisted and Enriched
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Topological states on fractal lattices
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Counting Rules of Nambu-Goldstone Modes
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
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• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Global Anomalies on the Hilbert Space
• Symmetric Mass Generation
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Realizing exceptional points of any order in the presence of symmetry
• Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models
• Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging
• Time-reversal symmetric U(1) quantum spin liquids
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Statistical translation invariance protects a topological insulator from interactions
• Symmetry indicators of band topology
• Cluster state as a non-invertible symmetry protected topological phase
• Composite Dirac liquids: parent states for symmetric surface topological order
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Classification of topological insulators and superconductors out of equilibrium
• Origin of fermion masses without spontaneous symmetry breaking
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Symmetry-Breaking Topological Insulators in the ${\mathbb{Z}}_2$ Bose-Hubbard Model
• Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Topological Time Crystals
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Composite fermion duality for half-filled multicomponent Landau Levels
• Experimental verification of the area law of mutual information in a quantum field simulator
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Bosonic integer quantum Hall effect in optical flux lattices
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Extraction of many-body Chern number from a single wave function
• Stabilizing multiple topological fermions on a quantum computer
• Relative Anomalies in (2+1)D Symmetry Enriched Topological States
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Generic coexistence of Fermi arcs and Dirac cones on the surface of time-reversal invariant Weyl semimetals
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• A Non-Perturbative Definition of the Standard Models
• Intertwined Topological Phases induced by Emergent Symmetry Protection
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Quasiparticle Interference Studies of Quantum Materials
• Topological and symmetry-enriched random quantum critical points
• All-fermion electrodynamics and fermion number anomaly inflow
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Interaction-induced topological properties of two bosons in flat-band systems
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases
• New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ${\mathbb{CP}}^{\mathrm{N}-1}$ Sigma Model
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• Hourglass semimetals with nonsymmorphic symmetries in three dimensions
• $(k,n)$-fractonic Maxwell theory
• Fermion masses through four-fermion condensates
• Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
• Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice
• Topological spin excitations in Harper-Heisenberg spin chains
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Quantum many-body topology of quasicrystals
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Self-organized topological insulator due to cavity-mediated correlated tunneling
• Fermion masses without symmetry breaking in two spacetime dimensions
• Lieb-Schultz-Mattis theorems for symmetry protected topological phases
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Relationship between Symmetry Protected Topological Phases and Boundary Conformal Field Theories via the Entanglement Spectrum
• Engineering interaction-induced topological insulators in a $\sqrt{3}\times \sqrt{3}$ substrate-induced honeycomb superlattice
• Gapless insulating edges of dirty interacting topological insulators
• Quantum Paramagnet and Frustrated Quantum Criticality in a Spin-One Diamond Lattice Antiferromagnet
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Symmetry enhanced boundary qubits at infinite temperature
• Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
• Classifying local fractal subsystem symmetry protected topological phases
• Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Topological edge modes without symmetry in quasiperiodically driven spin chains
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Quantum scars and bulk coherence in a symmetry-protected topological phase
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Dimensional hierarchy of fermionic interacting topological phases
• Many-body chiral edge currents and sliding phases of atomic spinwaves in momentum-space lattice
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Symmetry-protected dissipative preparation of matrix product states
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• Interacting topological quantum chemistry of Mott atomic limits
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Cobordism and Deformation Class of the Standard Model
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Topological spin ordering via Chern-Simons superconductivity
• Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
• Multiple band-crossings and Fermi surface topology: role of double nonsymmorphic symmetries in MnP-type crystal structures
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Topological phase in $1D$ topological Kondo insulator: $Z_2$ topological insulator, Haldane-like phase and Kondo breakdown
• Hidden order and symmetry protected topological states in quantum link ladders
• Quantum phase transition and critical behavior between the gapless topological phases
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Topology detection in cavity QED
• Ultra Unification
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Synthetic Flux Attachment
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Folding approach to topological orders enriched by mirror symmetry
• Lecture Notes on Topological Crystalline Insulators
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases
• Majorana zero modes induced by superconducting phase bias
• Realizing a symmetry protected topological phase through dimerized interactions
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Continuous phase transition between bosonic integer quantum Hall liquid and trivial insulator: evidences for deconfined quantum criticality
• Theory of oblique topological insulators
• Fermi Surface Symmetric Mass Generation
• Traversing double-well potential energy surfaces: photoinduced concurrent intralayer and interlayer structural transitions in XTe2 (X=Mo, W)
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Disentangling quantum matter with measurements
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Intrinsically Interacting Higher-Order Topological Superconductors
• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases
• Multiversality and Unnecessary Criticality in One Dimension
• Anomaly indicators for topological orders with $U(1)$ and time-reversal symmetry
• Observation of topological prethermal strong zero modes
• Surface field theories of point group symmetry protected topological phases
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Chern-Simons superconductors and their instabilities
• Ferromagnetic phase transition in topological crystalline insulator thin films: interplay of anomalous Hall angle and magnetic anisotropy
• Antiferromagnetic magnons from fractionalized excitations
• From orbifolding conformal field theories to gauging topological phases
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• The Curious Case of NiRh${}_2$O${}_4$: A Spin-Orbit Entangled Diamond Lattice Paramagnet
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Non-Liquid Cellular States
• Gauging (3+1)-dimensional topological phases: an approach from surface theories
• Edge modes and symmetry-protected topological states in open quantum systems
• Resilience of the topological phases to frustration
• Classification and construction of interacting fractonic higher-order topological phases
• Majorana zero modes and their bosonization
• Altermagnetic Instabilities from Quantum Geometry
• Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Worldsheet matter for electric flux strings
• Symmetry protected gapless $Z_2$ spin liquids
• Symmetry-protected topological phases and competing orders in a spin-1/2 XXZ ladder with a four-spin interaction
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Topological Dipole Conserving Insulators and Multipolar Responses
• Localization-Driven Correlated States of Two Isolated Interacting Helical Edges
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Dynamical enhancement of symmetries in many-body systems
• Landau theory of helical Fermi liquids
• Interacting topological mirror excitonic insulator in one dimension
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Femtosecond electron diffraction reveals local disorder and local anharmonicity in thermoelectric SnSe
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• 3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines
• Renormalization group approach to symmetry protected topological phases
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Lattice realization of a bosonic integer quantum Hall state - trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model
• Unconventional quantum phase transitions in a one-dimensional Lieb-Schultz-Mattis system
• Bilayer crystals of trapped ions for quantum information processing
• Screw dislocations in the X-cube fracton model
• Topological phases of parafermionic chains with symmetries
• Localized surfaces of three dimensional topological insulators
• Composite helical edges from Abelian fractional topological insulators
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Transverse Quantum Fluids
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Finite temperature physics of $1D$ topological Kondo insulator: Stable Haldane phase, Emergent energy scale and Beyond
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Accurate computations of Rashba spin-orbit coupling in interacting systems: from the Fermi gas to real materials
• Universal properties of the near-gap spectra of SmB6: dynamical mean-field calculations and photoemission experiments
• Symmetry-protection of multiphoton states of light
• Topologically enabled superconductivity
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Analysis of the unconventional chiral fermions in a non-centrosymmetric chiral crystal $\text{PtAl}$
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Topological zero modes and correlation pumping in an engineered Kondo lattice
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Exotic Invertible Phases with Higher-Group Symmetries
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Revisiting 2-pi phase slip suppression in topological Josephson junctions
• Effect of electronic band dispersion curvature on de Haas-van Alphen oscillations
• Superuniversality from disorder at two-dimensional topological phase transitions
• Emergent properties and the multiscale characterization challenge in condensed matter, from crystals to complex materials: a Review
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Ground-State Phase Diagram of the Bond-Alternating $S=2$ Quantum Spin Chain with the $XXZ$ and On-Site Anisotropies -- Symmetry Protected Topological Phase versus Trivial Phase
• A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography
• Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Classification of trivial spin-1 tensor network states on a square lattice
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Topological quantum criticality from multiplicative topological phases
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Is spontaneous vortex generation in superconducting 4Hb-TaS${}_2$ from vison-vortex nucleation with ${\mathbb{Z}}_2$ topological order?
• Fun with $F_{24}$
• Exact correlations in topological quantum chains
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Symmetry-protected topological phase transitions and robust chiral order on a tunable zigzag lattice
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Topological physics in quantum critical systems
• Gauge theory and mixed state criticality
• Second Euler number in four dimensional synthetic matter
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Universality and quantized response in bosonic nonfractionalized tunneling
• Synthesizing Weyl semimetals in weak topological insulator and topological crystalline insulator multilayers
• Interacting SPT phases are not Morita invariant
• Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
• Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion
• Observation of average topological phase in disordered Rydberg atom array
• Measurements of elastoresistance under pressure by combining in-situ tunable quasi-uniaxial stress with hydrostatic pressure
• Bound states of three fermions forming symmetry-protected topological phases
• Mirror anomaly in fermionic topological orders
• Renormalization view on resonance proliferation between many-body localized phases
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Edge Theories for Anyon Condensation Phase Transitions
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• A metronome spin stabilizes time-crystalline dynamics
• Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains
• The Weyl-Mott point: topological and non-Fermi liquid behavior from an isolated Green's function zero
• Topology and Spectrum in Measurement-Induced Phase Transitions
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Marginally localized edges of time-reversal symmetric topological superconductors
• A search for correlation-induced adiabatic paths between distinct topological insulators
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Topological switching in bilayer magnons via electrical control
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• Topologically protected states in $\delta$-doped junctions with band inversion
• Euler--Chern Correspondence via Topological Superconductivity
• Complete characterization of spin chains with two Ising symmetries
• Exotic $Z_2$ Symmetry Breaking Transitions in 2D Correlated Systems
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Topological Dipole Insulator
• Topological insulators and geometry of vector bundles
• Double band inversion in the topological phase transition of Ge1-xSnx alloys
• Quantum Restored Symmetry Protected Topological Phases
• Magnon topology driven by altermagnetism
• Finite-temperature spectroscopy of dirty helical Luttinger liquids
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Post-measurement Quantum Monte Carlo
• Quantum phase transitions in the alternating XY chain with three-site interactions
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Intertwined order of generalized global symmetries
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• SPT extension of $Z_2$ quantum Ising model's ferromagnetic phase
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Anomalies of global symmetries on the lattice
• Approximate recovery with locality and symmetry constraints
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Ultracold atomic lattice systems for simulating topological phases: A review
• Generalized symmetry enriched criticality in (3+1)d
• Hofstadter Butterflies in Topological Insulators
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice
• Theory of Hofstadter Superconductors
• Construction of Entangled Many-body States via the Higgs Mechanism
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• Twisted quantum doubles are sign problem-free
• Scaling of Computational Order Parameters in Rydberg Atom Graph States
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains
• Topological phases of bosons with local parity coupling on a dimerized lattice
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Hopf symmetry protected topological phases in the vicinity of spin orders
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems