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 (37)
- The density-matrix renormalization group in the age of matrix product states
- Generalized Global Symmetries
- Many body localization in Heisenberg XXZ magnet in a random field
- Entanglement and correlation functions following a local quench: a conformal field theory approach
- Quantum Noise as an Entanglement Meter
- Entanglement hamiltonians in two-dimensional conformal field theory
- Entanglement entropy of two disjoint blocks in XY chains
- Entanglement asymmetry as a probe of symmetry breaking
- Topological defects for the free boson CFT
- Intrinsically Gapless Topological Phases
- Quantum Dimension as Entanglement Entropy in 2D CFTs
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- 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
- Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
- 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
- Symmetry-resolved entanglement in critical non-Hermitian systems
- Broken global symmetries and defect conformal manifolds
- 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
- Quantized axial charge of staggered fermions and the chiral anomaly
- Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
- Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
- Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
- Universal entanglement signatures of interface conformal field theories
- 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