Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems

Abstract

The quantum Mpemba effect is the counter-intuitive non-equilibrium phenomenon wherein the dynamic restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking. The effect has been recently discovered theoretically and observed experimentally in the framework of global quantum quenches, but so far it has only been investigated in one-dimensional systems. Here we focus on a two-dimensional free-fermion lattice employing the entanglement asymmetry as a measure of symmetry breaking. Our investigation begins with the ground state analysis of a system featuring nearest-neighbor hoppings and superconducting pairings, the latter breaking explicitly the $U(1)$ particle number symmetry. We compute analytically the entanglement asymmetry of a periodic strip using dimensional reduction, an approach that allows us to adjust the extent of the transverse size, achieving a smooth crossover between one and two dimensions. Further applying the same method, we study the time evolution of the entanglement asymmetry after a quench to a Hamiltonian with only nearest-neighbor hoppings, preserving the particle number symmetry which is restored in the stationary state. We find that the quantum Mpemba effect is strongly affected by the size of the system in the transverse dimension, with the potential to either enhance or spoil the phenomenon depending on the initial states. We establish the conditions for its occurrence based on the properties of the initial configurations, extending the criteria found in the one-dimensional case.

arXiv comment18 pages, 8 figures. Minor clarifications, typos corrected. Final version published in Phys. Rev. B

References in corpus (47)

• Many-Body Physics with Ultracold Gases
• Nonequilibrium dynamics of closed interacting quantum systems
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Calculation of reduced density matrices from correlation functions
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Reduced Density Matrix after a Quantum Quench
• Entanglement dynamics after quantum quenches in generic integrable systems
• Anomalous cooling and heating - the Mpemba effect and its inverse
• Lecture notes on Generalised Hydrodynamics
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids
• Exponentially faster cooling in a colloidal system
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement asymmetry as a probe of symmetry breaking
• Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect
• The Mpemba index and anomalous relaxation
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Microscopic origin of the quantum Mpemba effect in integrable systems
• Quantum Mpemba effect in a quantum dot with reservoirs
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Lindblad dissipative dynamics in presence of phase coexistence
• On Density-Matrix Spectra for Two-Dimensional Quantum Systems
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
• Quantum Noise Analysis of Spin Systems Realized with Cold Atoms
• Full Counting Statistics in the Transverse Field Ising Chain
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Anomalous heating in a colloidal system
• Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Excited state entanglement in homogeneous fermionic chains
• Hyper-acceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment
• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Relaxation shortcuts through boundary coupling
• Dynamics of charge fluctuations from asymmetric initial states
• Quenches across the self-organization transition in multimode cavities
• Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
• Symmetric inseparability and number entanglement in charge conserving mixed states
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Realistic protocol to measure entanglement at finite temperatures
• Quench dynamics in lattices above one dimension: the free fermionic case

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• Symmetry Breaking Dynamics in Quantum Many-Body Systems
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• Translation symmetry restoration in integrable systems: the noninteracting case
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• Non-Abelian entanglement asymmetry in random states
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• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
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• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
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