Generalized Symmetries in Condensed Matter

Abstract

Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This is a brief and elementary review of some of these developments.

27 pages + refs; v2: added refs, minor improvements; v3: corrected a statement about the relation between SSB of higher-form symmetry and topological order, added an appendix explaining a counterexample, based on 2305.07063

References in corpus (10)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Interacting anyons in topological quantum liquids: The golden chain
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Vortex-boson duality in four space-time dimensions
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions

Cited by in corpus (175)

• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Average Symmetry-Protected Topological Phases
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Lecture Notes on Generalized Symmetries and Applications
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Symmetric Mass Generation
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Anomalies and Symmetry Fractionalization
• Cluster state as a non-invertible symmetry protected topological phase
• An Introduction to Higher-Form Symmetries
• Intrinsic Mixed-state Topological Order
• Bootstrapping Non-Invertible Symmetries
• Symmetry protected topological phases under decoherence
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Experimental signatures of quantum and topological states in frustrated magnetism
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Exact emergent higher-form symmetries in bosonic lattice models
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Topological holography, quantum criticality, and boundary states
• From Symmetries to Commutant Algebras in Standard Hamiltonians
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Quantization of Axion-Gauge Couplings and Non-Invertible Higher Symmetries
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Fermionization of fusion category symmetries in 1+1 dimensions
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generating Lattice Non-invertible Symmetries
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• A Chern-Simons theory for dipole symmetry
• Approximate higher-form symmetries, topological defects, and dynamical phase transitions
• A symmetry principle for gauge theories with fractons
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Composing topological domain walls and anyon mobility
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Theory of oblique topological insulators
• Fermionic Higher-form Symmetries
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Topological defects
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• (SPT-)LSM theorems from projective non-invertible symmetries
• Entanglement entropy as an order parameter for strongly coupled nodal line semimetals
• Higher-form Symmetries under Weak Measurement
• High-Quality Axions from Higher-Form Symmetries in Extra Dimensions
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Gauging non-invertible symmetries on the lattice
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• High spin axion insulator
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Fractons on Graphs and Complexity
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the Rényi-1 Correlator
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Topological Defects in Floquet Circuits
• Definition and Classification of Fermi Surface Anomalies
• Higher-form symmetries, anomalous magnetohydrodynamics, and holography
• Gauge Invariance and Anomalies in Condensed Matter Physics
• Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
• Non-Fermi Liquids from Dipolar Symmetry Breaking
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Zero sound and higher-form symmetries in compressible holographic phases
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Categorical-Symmetry Resolved Entanglement in CFT
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Symmetry Transmutation and Anomaly Matching
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Gapless higher-order topology and corner states in Floquet systems
• Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
• Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Deconfined quantum phase transition on the kagome lattice: Distinct velocities of spinon and string excitations
• Topological aspects of brane fields: solitons and higher-form symmetries
• Additivity, Haag duality, and non-invertible symmetries
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Fusion rules and shrinking rules of topological orders in five dimensions
• Quantum Cluster State Model with Haagerup Fusion Category Symmetry
• Interplay between lattice gauge theory and subsystem codes
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Towards absolutely stable ergodicity breaking in two and three dimensions
• Bipartite Fluctuations of Critical Fermi Surfaces
• Robust Hilbert space fragmentation in group-valued loop models
• A post-Gaussian approach to dipole symmetries and interacting fractons
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Impossible Symmetries and Conformal Gravity
• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Isolated zero mode in a quantum computer from a duality twist
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Edge Theories for Anyon Condensation Phase Transitions
• Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
• Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Anyon condensation in mixed-state topological order
• Higgs Phases and Boundary Criticality
• Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
• Higher-group global symmetry and the bosonic M5 brane
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Note on lattice description of generalized symmetries in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Non-Invertible Gauss Law and Axions
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Generalized Landau Paradigm for quantum phases and phase transitions
• Quantum colored strings in the hole-doped $t$-$J_z$ model
• Disentangling anomaly-free symmetries of quantum spin chains
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Fractonic superfluids. III. Hybridizing higher moments
• Covariant field theory of 3D massive fractons
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Deconfined Quantum Critical Point with Non-locality
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Exploring two dimensional ${\mathbb{Z}}_2$ invariant phases with time reversal symmetry and their transitions with topological operations
• The Luttinger Count is the Homotopy not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids
• Threefold Way for Typical Entanglement
• Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal
• Chiral Edge States Emerging on Anyon-Net
• Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions
• Intertwined order of generalized global symmetries
• Entropic Order Parameters for Categorical Symmetries in 2D-CFT
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Entropic order parameters and topological holography
• Les Houches Lecture Notes on Tensor Networks
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice
• Holographic duality between bulk topological order and boundary mixed-state order
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Topological entanglement entropy meets holographic entropy inequalities
• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Discrete time crystal order in spin chains enabled by Floquet flat bands
• Covariant Fracton Electrodynamics in Six Dimensions
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Generalized symmetry enriched criticality in (3+1)d
• Higher-form entanglement asymmetry and topological order
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains
• Entanglement Spectrum Resolved by Loop Symmetries