LSM and CPT

Abstract

We study a number of 1+1d lattice models with anti-unitary symmetries that simultaneously reflect space and reverse time. Some of these symmetries are anomalous, leading to Lieb-Schultz-Mattis-type constraints, thus excluding a trivially gapped phase. Examples include a mod 8 anomaly in the Majorana chain and various mod 2 anomalies in the spin chain. In some cases, there is an exact, non-anomalous lattice symmetry that flows in the continuum to CPT. In some other cases, the CPT symmetry of the continuum theory is emergent or absent. Depending on the model, the anomaly of the lattice model is matched in the continuum in different ways. In particular, it can be mapped to an emergent anomaly of an emanant symmetry.

46 pages plus appendices, 3 figures, 4 tables

References in corpus (76)

• Classification of topological insulators and superconductors in three spatial dimensions
• Periodic table for topological insulators and superconductors
• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Braiding statistics approach to symmetry-protected topological phases
• The effects of interactions on the topological classification of free fermion systems
• Fermion Path Integrals And Topological Phases
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• On finite symmetries and their gauging in two dimensions
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Kramers-Wannier duality from conformal defects
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Topological Defects on the Lattice I: The Ising model
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Interacting topological phases and modular invariance
• Reflection positivity and invertible topological phases
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• The "Parity" Anomaly On An Unorientable Manifold
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Intrinsic and emergent anomalies at deconfined critical points
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Intrinsically Gapless Topological Phases
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Setting the quantum integrand of M-theory
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Phase Diagram of the Interacting Majorana Chain Model
• 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
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Anomalies and Bounds on Charged Operators
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• All Majorana Models with Translation Symmetry are Supersymmetric
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Cluster state as a non-invertible symmetry protected topological phase
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• C-P-T anomaly matching in bosonic quantum field theory and spin chains
• Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• 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
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Conformal fields and operator product expansion in critical quantum spin chains
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• Exactly solvable model for a deconfined quantum critical point in 1D
• Topological Superconductors on Superstring Worldsheets
• Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Mixed global anomalies and boundary conformal field theories
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• GSO projections via SPT phases
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Quantized axial charge of staggered fermions and the chiral anomaly
• Long-range spin chirality dimer order in the Heisenberg chain with modulated Dzyaloshinskii-Moriya interactions
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Global anomaly detection in two-dimensional symmetry-protected topological phases
• Anomalies and unnatural stability of multi-component Luttinger liquids in ${\mathbb{Z}}_n\times {\mathbb{Z}}_n$ spin chains
• Symmetry Transmutation and Anomaly Matching
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries
• Anomalous Continuous Translations
• LSM and CPT

Cited by in corpus (2)

• LSM and CPT
• Symmetry-Enforced Fermi Surfaces