Global anomaly detection in two-dimensional symmetry-protected topological phases

Abstract

Edge theories of symmetry-protected topological phases are well-known to possess global symmetry anomalies. In this work we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyse the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.

References in corpus (35)

• Entanglement Entropy and Quantum Field Theory
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• 2D symmetry protected topological orders and their protected gapless edge excitations
• TFT construction of RCFT correlators I: Partition functions
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Duality and defects in rational conformal field theory
• Generalised twisted partition functions
• Scaling of entanglement support for Matrix Product States
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• Permeable conformal walls and holography
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Topological Defects on the Lattice I: The Ising model
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Interacting topological phases and modular invariance
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Topological defects for the free boson CFT
• Wave Function and Strange Correlator of Short Range Entangled states
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Topological conformal defects with tensor networks
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Detecting two dimensional symmetry protected topological order in a ground state wave function
• Fermionic projected entangled-pair states and topological phases
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Chiral symmetry on the edge of 2D symmetry protected topological phases
• Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
• Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories
• MERA for Spin Chains with Continuously Varying Criticality
• Symmetry-protected many-body Aharonov-Bohm effect
• Anomalies and entanglement renormalization

Cited by in corpus (18)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Quantum criticality under decoherence or weak measurement
• Lecture Notes on Generalized Symmetries and Applications
• Mapping topological to conformal field theories through strange correlators
• Symmetry protected topological phases under decoherence
• Symmetry-protected sign problem and magic in quantum phases of matter
• Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation
• Mixed global anomalies and boundary conformal field theories
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Anomalous domain wall condensation in a modified Ising chain
• LSM and CPT
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Effective Conformal Field Theory generated from Pure and Dephased Chern insulator
• Les Houches Lecture Notes on Tensor Networks