Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space

Abstract

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented as a matrix product operator. Importantly, unlike its continuum counterpart, the symmetry algebra involves lattice translations. Consequently, it is not described by a fusion category. In the presence of this defect, the symmetry algebra involving parity/time-reversal is realized projectively, which is reminiscent of an anomaly. Different Hamiltonians with the same lattice non-invertible symmetry can flow in their continuum limits to infinitely many different fusion categories (with different Frobenius-Schur indicators), including, as a special case, the Ising CFT. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the lattice non-invertible symmetry.

arXiv comment115 pages, 5 figures, 6 tables; v2: minor revision

References in corpus (127)

• Anyons in an exactly solved model and beyond
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Generalized Global Symmetries
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Lieb-Schultz-Mattis in Higher Dimensions
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Interacting anyons in topological quantum liquids: The golden chain
• TFT construction of RCFT correlators I: Partition functions
• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• Duality and defects in rational conformal field theory
• Generalized Symmetries in Condensed Matter
• Generalised twisted partition functions
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• On finite symmetries and their gauging in two dimensions
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Kramers-Wannier duality from conformal defects
• Non-Invertible Duality Defects in 3+1 Dimensions
• Symmetries and Strings of Adjoint QCD${}_2$
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Topological Defects on the Lattice I: The Ising model
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• TFT construction of RCFT correlators III: Simple currents
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Building crystalline topological phases from lower-dimensional states
• Non-perturbative approach to Luttinger's theorem in one dimension
• Gauging spatial symmetries and the classification of topological crystalline phases
• Defect lines, dualities, and generalised orbifolds
• A short introduction to Fibonacci anyon models
• Intrinsic and emergent anomalies at deconfined critical points
• Anyons and matrix product operator algebras
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Gauging quantum states: from global to local symmetries in many-body systems
• Efficient variational simulation of non-trivial quantum states
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• TFT construction of RCFT correlators II: Unoriented world sheets
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Phase Diagram of the Interacting Majorana Chain Model
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• Topological Transition on the Conformal Manifold
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Orbifold completion of defect bicategories
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Topological Defects on the Lattice: Dualities and Degeneracies
• Long-range entanglement from measuring symmetry-protected topological phases
• Anomalies and Bounds on Charged Operators
• D-branes and K-theory in 2D topological field theory
• Exploring Non-Invertible Symmetries in Free Theories
• Fermionic minimal models
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• All Majorana Models with Translation Symmetry are Supersymmetric
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Non-Invertible Duality Transformation Between SPT and SSB Phases
• On lattice models of gapped phases with fusion category symmetries
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Dualities in one-dimensional quantum lattice models: topological sectors
• Topological conformal defects with tensor networks
• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Quantum circuit complexity of one-dimensional topological phases
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Bootstrapping Non-Invertible Symmetries
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• A many-body index for quantum charge transport
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Subsystem Non-Invertible Symmetry Operators and Defects
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Topological field theories and symmetry protected topological phases with fusion category symmetries
• Invertible defects and isomorphisms of rational CFTs
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
• Introduction to Generalized Global Symmetries in QFT and Particle Physics
• Discrete torsion defects
• Sequential Quantum Circuits as Maps between Gapped Phases
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Classifying phases protected by matrix product operator symmetries using matrix product states
• Topological Field Theory with Haagerup Symmetry
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• Non-zero momentum requires long-range entanglement
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Classification and construction of unitary topological field theories in two dimensions
• Orbifolds and topological defects
• Mixed global anomalies and boundary conformal field theories
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Quantum Criticality in Topological Insulators and Superconductors: Emergence of Strongly Coupled Majoranas and Supersymmetry
• Anomalies of $(1+1)D$ categorical symmetries
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Fermionization and boundary states in 1+1 dimensions
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Constraints on order and disorder parameters in quantum spin chains
• Anomalies of non-invertible self-duality symmetries: fractionalization and gauging
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Classification of fractional quantum Hall states with spatial symmetries
• Topological Defects in Floquet Circuits
• Categorical Landau Paradigm for Gapped Phases
• Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states
• TFT construction of RCFT correlators V: Proof of modular invariance and factorisation
• Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
• The Lieb-Schultz-Mattis Theorem: A Topological Point of View
• Lattice Realizations of Topological Defects in the critical (1+1)-d Three-State Potts Model

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• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Global symmetries of quantum lattice models under non-invertible dualities
• Self-$G$-ality in 1+1 dimensions
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• Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Duality-preserving deformation of 3+1d lattice ${\mathbb{Z}}_2$ gauge theory with exact gapped ground states
• Preparing matrix product states via fusion: constraints and extensions
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Isolated zero mode in a quantum computer from a duality twist
• Duality defect in a deformed transverse-field Ising model
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• ${\mathbb{Z}}_2$ gauging and self-dualities of the $XX$ model and its cousins
• Many-body quantum catalysts for transforming between phases of matter
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Fractonic criticality in Rydberg atom arrays
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• $N$-ality symmetry and SPT phases in (1+1)d
• From gauging to duality in one-dimensional quantum lattice models
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains