Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain

Abstract

The entanglement asymmetry is a novel quantity that, using entanglement methods, measures how much a symmetry is broken in a part of an extended quantum system. So far it has only been used to characterise the breaking of continuous Abelian symmetries. In this paper, we extend the concept to cyclic ${\mathbb{Z}}_N$ groups. As an application, we consider the XY spin chain, in which the ground state spontaneously breaks the ${\mathbb{Z}}_2$ spin parity symmetry in the ferromagnetic phase. We thoroughly investigate the non-equilibrium dynamics of this symmetry after a global quantum quench, generalising known results for the standard order parameter.

arXiv comment37 pages, 15 figures. Minor corrections and comments added, new figure. Final version published in JSTAT

References in corpus (53)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Calculation of reduced density matrices from correlation functions
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Probing entanglement entropy via randomized measurements
• Probing entanglement in a many-body-localized system
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• The randomized measurement toolbox
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Reduced Density Matrix after a Quantum Quench
• Quench dynamics across quantum critical points
• Symmetry-resolved entanglement in many-body systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Dynamical Correlations after a Quantum Quench
• Equipartition of the Entanglement Entropy
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement asymmetry as a probe of symmetry breaking
• Long range correlations in the non-equilibrium quantum relaxation of a spin chain
• Symmetry resolved entanglement in free fermionic systems
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Imbalance Entanglement: Symmetry Decomposition of Negativity
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Identification of symmetry-protected topological states on noisy quantum computers
• Quantum relaxation after a quench in systems with boundaries
• Probing scrambling using statistical correlations between randomized measurements
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Symmetry resolved entanglement: Exact results in 1D and beyond
• Symmetry decomposition of negativity of massless free fermions
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
• Quantum quenches from excited states in the Ising chain
• Full Counting Statistics in the Transverse Field Ising Chain
• Entanglement barrier and its symmetry resolution: theory and experiment
• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Symmetry-resolved Page curves
• Stationary entropies after a quench from excited states in the Ising chain
• Dynamics of charge fluctuations from asymmetric initial states
• Symmetric inseparability and number entanglement in charge conserving mixed states
• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Realistic protocol to measure entanglement at finite temperatures
• Two-Point Functions of Composite Twist Fields in the Ising Field Theory
• Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Boundary Symmetry Breaking in CFT and the String Order Parameter

Cited by in corpus (42)

• 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
• The quantum Mpemba effects
• Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect
• Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
• The quantum Mpemba effect in free-fermionic mixed states
• Speedups in nonequilibrium thermal relaxation: Mpemba and related effects
• A universal formula for the entanglement asymmetry of matrix product states
• Translation symmetry restoration under random unitary dynamics
• Non-equilibrium dynamics of charged dual-unitary circuits
• An entanglement asymmetry study of black hole radiation
• Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
• Quantum Mpemba Effects from Symmetry Perspectives
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits
• Entanglement asymmetry in the critical XXZ spin chain
• Entanglement asymmetry and symmetry defects in boundary conformal field theory
• Entanglement asymmetry in conformal field theory and holography
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• A simpler probe of the quantum Mpemba effect in closed systems
• Entanglement asymmetry dynamics in random quantum circuits
• More on symmetry resolved operator entanglement
• Quench dynamics in lattices above one dimension: the free fermionic case
• Quantum Mpemba effect in parity-time symmetric systems
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Translation symmetry restoration in integrable systems: the noninteracting case
• Non-Abelian entanglement asymmetry in random states
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• A resource theoretical unification of Mpemba effects: classical and quantum
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Breaking global symmetries with locality-preserving operations
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Extracting the symmetries of nonequilibrium quantum many-body systems
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices