Entanglement asymmetry and symmetry defects in boundary conformal field theory

Abstract

A state in a quantum system with a given global symmetry, $G$, can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the $G-$symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the "distance" between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group $G$ and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.

29 pages, 7 figures

References in corpus (32)

• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Entanglement hamiltonians in two-dimensional conformal field theory
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Entanglement asymmetry as a probe of symmetry breaking
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Physics at the entangling surface
• Microscopic origin of the quantum Mpemba effect in integrable systems
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
• Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems
• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Entropic order parameters for the phases of QFT
• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Dynamics of charge fluctuations from asymmetric initial states
• Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect
• Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
• Left-Right Entanglement Entropy of Boundary States
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• A universal formula for the entanglement asymmetry of matrix product states
• An entanglement asymmetry study of black hole radiation
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
• Proof of the universal density of charged states in QFT
• A universal formula for the density of states in theories with finite-group symmetry
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• A universal formula for the density of states with continuous symmetry
• Symmetry-resolved modular correlation functions in free fermionic theories
• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Universal information of critical quantum spin chains from wavefunction overlaps
• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach

Cited by in corpus (9)

• A simpler probe of the quantum Mpemba effect in closed systems
• Entanglement asymmetry dynamics in random quantum circuits
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Non-Abelian entanglement asymmetry in random states
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Entropic order parameters and topological holography
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group