Zoo of quantum-topological phases of matter

Abstract

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature. But those disordered liquids actually can have rich patterns of many-body entanglement representing new kinds of order. This paper will give a simple introduction and a brief survey of topological phases of matter. We will first discuss topological phases that have topological order (ie with long range entanglement). Then we will cover topological phases that have no topological order (ie with only short-range entanglement).

18 pages, 8 figures, 4 tables. A short review, expanded version

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• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
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• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
• Theory of topological spin Josephson junctions
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Origin of Topological Order in a Cooper Pair Insulator
• Pivoting through the chiral-clock family
• Emergent Gauge Fields in Band Insulators
• Wegner-Wilson loops in string nets
• Steady-state topological order
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Thermal state entanglement entropy on a quantum graph
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Fusion rules and shrinking rules of topological orders in five dimensions
• Finite-temperature quantum topological order in three dimensions
• New disordered anyon phase of doped graphene zigzag nanoribbon
• The case of SU$(3)$ criticality in spin-2 chains
• Electric field control of a quantum spin liquid in weak Mott insulators
• Predicting Topological Entanglement Entropy in a Rydberg analog simulator
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Quantum spin liquid from electron-phonon coupling
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Bipartite Fluctuations of Critical Fermi Surfaces
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Fractional quantum Hall effect of Bose-Fermi mixtures
• Inelastic neutron scattering study of the anisotropic $S=1$ spin chain [Ni(HF${}_2$)(3-Clpyridine)${}_4$]BF${}_4$
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Learning quantum dissipation by the neural ordinary differential equation
• Liouvillian skin effect in quantum neural networks
• Topological physics in quantum critical systems
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Kitaev model in regular hyperbolic tilings
• Second Euler number in four dimensional synthetic matter
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Multi-particle interferometry in the time-energy domain with localized topological quasiparticles
• Inverted c-functions in thermal states
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Quantum Simulation of Spin-1 XXZ-Heisenberg Models and the Haldane Phase with Dysprosium
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Machine learning of mirror skin effects in the presence of disorder
• Petz map recovery for long-range entangled quantum many-body states
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Exploring the topological sector optimization on quantum computers
• Topology of Discrete Quantum Feedback Control
• Topological states in strongly correlated systems
• Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Geometric test for topological states of matter
• Edge Theories for Anyon Condensation Phase Transitions
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Topological phases of amorphous matter
• Kibble-Zurek mechanism in quantum link model
• Topological states constructed by two different trivial quantum wires
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Duality defect in a deformed transverse-field Ising model
• Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Haldane and Dimer phases in a frustrated spin chain: an exact groundstate and associated topological phase transition
• Hardness of observing strong-to-weak symmetry breaking
• Exciton Berryology
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach
• Spin-lattice Coupling in U(1) Quantum Spin Liquids
• Ising versus $SU(2{)}_2$ string-net ladder
• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Classifying parafermionic gapped phases using matrix product states
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling
• Finite-temperature properties of string-net models
• Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Quark-Gluon Plasma and Nucleons a la Laughlin
• Finite-temperature topological invariant for higher-order topological insulators
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices
• Survey on Computational Applications of Tensor Network Simulations
• Euler--Chern Correspondence via Topological Superconductivity
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Topological Burning Glass Effect
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Dihedral twist liquid models from emergent Majorana fermions
• Confinement and oscillating deconfinement crossover of two-magnon excitations in quantum spin chains quantified by spin entanglement entropy
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Topological Anderson insulators by latent symmetry
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Quantum Spin Liquid phases in Kitaev Materials
• The destiny of obstructed atomic insulator under correlation
• Nature of the 1/3 Magnetization Plateau in Spin-1/2 Kagome Antiferromagnets
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Topological bosonic states on ribbons of honeycomb lattice
• Topologically protected states in $\delta$-doped junctions with band inversion
• Exotic $Z_2$ Symmetry Breaking Transitions in 2D Correlated Systems
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Brane order and quantum magnetism in modulated anisotropic ladders
• Quantum Gauge Networks: A New Kind of Tensor Network
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• The nature of low-temperature spin-freezing in frustrated Kitaev magnets
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Modular extension of topological orders from congruence representations
• Selective branching, quenching, and converting of topological modes
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Measurement-invisible quantum correlations in scrambling dynamics
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• Partially topological phase in a quantum loop gas model with tension and pressure
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Topology in the space-time scaling limit of quantum dynamics
• Non-Abelian Anyons with Rydberg Atoms
• Scaling of entanglement entropy at quantum critical points in random spin chains
• Magnon topology driven by altermagnetism
• Bilayer, hydrogenated and fluorinated graphene: QED vs SU(2) QCD theory
• Zero Curvature Condition for Quantum Criticality
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Promising regimes for the observation of topological degeneracy in spin chains
• Robust spin liquid state against magnetic-dilution in the bi-layer Kagome material Ca${}_{10}$Cr${}_7$O${}_{28}$
• Topological Triviality of Flat Hamiltonians
• Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Robust translational invariance in topological bands against lattice potentials and disorders
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• Quantum Signatures of Topological Phase in Bosonic Quadratic System
• Fractons on the edge
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Double band inversion in the topological phase transition of Ge1-xSnx alloys
• Topological order in symmetric blockade structures
• Non-Linear Interference Challenging Topological Protection of Chiral Edge States
• Degenerate Topological Edge States in Multimer Chains
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• Symmetry-Enforced Fermi Surfaces
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets
• Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Extended string-net models with all anyons at finite temperature
• Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator
• Quantum phase transitions in the alternating XY chain with three-site interactions
• Extended Haldane model -- a modern gateway to topological insulators
• Unsupervised Learning of Symmetry Protected Topological Phase Transitions
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• Instantons and topological order in two-leg electron ladders: A universality class
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• Quantum Hall Effect without Chern Bands
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Superactivation of Bell nonlocality in pure anyonic states
• Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach
• Topological band insulators without translational symmetry
• Fractional Quantum Hall States on CP2 Space
• Simulating Topological Order on Quantum Processors
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• The Physics of Quantum 2.0: Challenges in understanding Quantum Matter
• Three-component fractional quantum Hall effect in topological flat bands
• Les Houches Lecture Notes on Tensor Networks
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Boundary condition and reflection anomaly in $2+1$ dimensions
• SPT extension of $Z_2$ quantum Ising model's ferromagnetic phase
• Quantum anomalous Hall effect with high Chern number in two dimensional ferromagnets Ti2TeSO
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Quantum criticality and confinement in weak Mott insulators
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Entanglement Spectrum Resolved by Loop Symmetries
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Devil's staircase of topological Peierls insulators and Peierls supersolids
• Central Charge in Quantum Optics
• Transport through Nodal Surface Semimetal-Superconductor junction in absence/presence of light irradiation
• Entanglement transition in a cluster spin chain coupled with free spins
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states
• Higher-order topological quantum paramagnets
• Swinging small quantum systems out of available values of control parameters
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Emergent quasi-particles of spin-1 trimer chain
• Coupled-wire construction of non-Abelian higher-order topological phases
• Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry
• Nonlocality-induced surface localization in Bose-Einstein condensates of light
• Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Non-self-averaging topological Anderson insulator
• Measuring entanglement without local addressing in quantum many-body simulators via spiral quantum state tomography
• Topological Dislocation Response in Elementary Semiconductors
• Hidden subsystem symmetry protected states in competing topological orders
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Theory of Hofstadter Superconductors
• Parafermionic representation of Potts-based cluster chain
• Peratic Phase Transition by Bulk-to-Surface Response
• Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions
• The index of a pair of pure states and the interacting integer quantum Hall effect
• Introduction to abelian anyons in planar systems
• Direct Evidence for Fermi Statistics from Proximity to the Kitaev Spin Liquid in RuCl3
• Ultracold atomic lattice systems for simulating topological phases: A review
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Entanglement entropy as a probe of topological phase transitions
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order