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.

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

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• 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
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• Non-equilibrium dynamics of charged dual-unitary circuits
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• Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
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• 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
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• 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