Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
arXiv:2410.16402 · doi:10.1103/PhysRevB.111.165121
Abstract
The global symmetry, either invertible or non-invertible, has been extensively studied in two dimensional conformal field theories in recent years. When the theory is defined on a manifold with open boundaries, however, many interesting conformal boundary conditions will fully or partially break such global symmetry. In this work, we study the effect of symmetry-breaking boundaries or interfaces when the system is out of equilibrium. We show that the boundary or interface symmetry-breaking can be detected by the time evolution of string order parameters, which are constructed from the symmetry operators that implement the symmetry transformations. While the string order parameters are independent of time if the symmetry is preserved over the whole system, they evolve in time in a universal way if the boundary or interface breaks the symmetry. More explicitly, in the presence of boundary or interface symmetry-breaking, the string order parameters decay exponentially in time after a global quantum quench, and decay as a power-law in time after a local quantum quench. We also generalize our study to the case when the string order parameters are defined in a subsystem, which are related to the full counting statistics. It is found there are also universal features in the time evolution of string order parameters in this case. We verify our field theory results by studying the time evolution of these two different types of string order parameters in lattice models.
are welcome. 32 pages, many figures; v2: Refs added
References in corpus (86)
- The density-matrix renormalization group in the age of matrix product states
- Generalized Global Symmetries
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Unbounded growth of entanglement in models of many-body localization
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- Many body localization in Heisenberg XXZ magnet in a random field
- Electron Counting Statistics and Coherent States of Electric Current
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Locally Localized Gravity
- Quantum Quenches in Extended Systems
- Universal slow growth of entanglement in interacting strongly disordered systems
- Measurement-driven entanglement transition in hybrid quantum circuits
- Discrete time crystals: rigidity, criticality, and realizations
- Topological Defect Lines and Renormalization Group Flows in Two Dimensions
- Entanglement and correlation functions following a local quench: a conformal field theory approach
- Quantum Noise as an Entanglement Meter
- Detection of Symmetry Protected Topological Phases in 1D
- Generalised twisted partition functions
- Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
- Permeable conformal walls and holography
- Out-of-Time-Order Correlation for Many-Body Localization
- Kramers-Wannier duality from conformal defects
- Symmetry-resolved entanglement in many-body systems
- Entanglement hamiltonians in two-dimensional conformal field theory
- Holographic Local Quenches and Entanglement Density
- D-Brane Instantons and K-Theory Charges
- Quantum Entanglement of Local Operators in Conformal Field Theories
- Entanglement entropy of two disjoint blocks in XY chains
- Entanglement asymmetry as a probe of symmetry breaking
- Reduced density matrix and internal dynamics for multicomponent regions
- Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
- Geometrical interpretation of D-branes in gauged WZW models
- Gapless topological phases and symmetry-enriched quantum criticality
- Topological defects for the free boson CFT
- Intrinsically Gapless Topological Phases
- Reflection and Transmission for Conformal Defects
- Quantum Dimension as Entanglement Entropy in 2D CFTs
- Symmetry resolved entanglement in free fermionic systems
- Conformal boundary states for free bosons and fermions
- Symmetry breaking boundaries I. General theory
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- Full Current Statistics in Diffusive Normal-Superconductor Structures
- Symmetry breaking boundaries II. More structures; examples
- Entanglement through conformal interfaces
- Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
- Non-Invertible Duality Transformation Between SPT and SSB Phases
- Full Counting Statistics in the Transverse Field Ising Chain
- Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
- Symmetry Breaking Boundary States and Defect Lines
- Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
- The hidden symmetry-breaking picture of symmetry-protected topological order
- Emergent Black Hole Dynamics in Critical Floquet Systems
- Floquet Quantum Criticality
- Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
- Geometric approach to inhomogeneous Floquet systems
- Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
- A note on the Full Counting Statistics of paired fermions
- Floquet conformal field theories with generally deformed Hamiltonians
- Exact results for the entanglement across defects in critical chains
- From symmetry-protected topological order to Landau order
- Symmetry-resolved entanglement in critical non-Hermitian systems
- Universal Entanglement Spectra of Gapped One-dimensional Field Theories
- Broken global symmetries and defect conformal manifolds
- Entanglement hamiltonian evolution during thermalization in conformal field theory
- Topological and symmetry-enriched random quantum critical points
- Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories
- Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
- The fine structure of heating in a quasiperiodically driven critical quantum system
- Classification of deformed Floquet Conformal Field Theories
- Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
- Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
- Central Charge of Periodically Driven Critical Kitaev Chains
- Charged Topological Entanglement Entropy
- Quantized axial charge of staggered fermions and the chiral anomaly
- Entanglement evolution across a conformal interface
- Open topological defects and boundary RG flows
- Extreme boundary conditions and random tilings
- Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
- Boundary RG Flows for Fermions and the Mod 2 Anomaly
- Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
- Universal entanglement signatures of interface conformal field theories
- Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
- Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
- Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
- Boundary Symmetry Breaking in CFT and the String Order Parameter