Entanglement asymmetry and quantum Mpemba effect in the XY spin chain

Abstract

Entanglement asymmetry is a quantity recently introduced to measure how much a symmetry is broken in a part of an extended quantum system. It has been employed to analyze the non-equilibrium dynamics of a broken symmetry after a global quantum quench with a Hamiltonian that preserves it. In this work, we carry out a comprehensive analysis of the entanglement asymmetry at equilibrium taking the ground state of the XY spin chain, which breaks the U(1) particle number symmetry, and provide a physical interpretation of it in terms of superconducting Cooper pairs. We also consider quenches from this ground state to the XX spin chain, which preserves the U(1) symmetry. In this case, the entanglement asymmetry reveals that the more the symmetry is initially broken, the faster it may be restored in a subsystem, a surprising and counter-intuitive phenomenon that is a type of a quantum Mpemba effect. We obtain a quasi-particle picture for the entanglement asymmetry in terms of Cooper pairs, from which we derive the microscopic conditions to observe the quantum Mpemba effect in this system, giving further support to the criteria recently proposed for arbitrary integrable quantum systems. In addition, we find that the power law governing symmetry restoration depends discontinuously on whether the initial state is critical or not, leading to new forms of strong and weak Mpemba effects.

Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems

“…Classical Mpemba effect was observed also in several other systems, such as clathrate hydrates [16], magnetic alloys [17], carbon nanotube resonators [18], granular gases [19], colloidal systems [20] or dilute atomic gases [21]. A microscopic explanation of the quantum Mpemba effect in both interacting and free integrable spin chains has been provided in [5] (see also [9] for a further study of the asymmetry in free integrable quantum systems).…”

“…from the tilted ferromagnetic state [1], and, more in general, from the ground state of the XY spin chain [9], which does not preserve the transverse magnetization. In these situations, the dynamics determined by a free U (1)-invariant Hamiltonian leads to the symmetry restoration of the U (1) charge in the subsystem.…”

“…Indeed, the concepts of symmetry and symmetry-breaking are ubiquitous in Physics. In recent years there has been renewed interest in studying symmetry-breaking both in and out-of-equilibrium systems [1][2][3][4][5][6][7][8][9][10][11]. Let us consider the prototypical setup of the quantum quench [12] in which a system, here a one-dimensional one, is prepared in an initial state and let to evolve under a many-body Hamiltonian H. Let us also assume that the Hamiltonian commutes with a charge operator Q, which generates an Abelian symmetry U (1).…”

“…Crucially, the dynamics of the entanglement asymmetry, and the onset of the quantum Mpemba effect, can be understood in the space-time scaling limit (hydrodynamic limit) ℓ, t → ∞ with the ratio t/ℓ fixed. Indeed, the main formula obtained in [1,9] is reminiscent of the socalled quasiparticle picture [26][27][28][29] for the entanglement entropy. Still, a full-fledged quasiparticle picture was not available so far.…”

“…Here we first review the results of [1,2,9]. We focus on a dynamics governed by the XX chain, considering quantum quenches from the ground state of the XY chain and the tilted Néel state.…”