[Paper Review] The quantum Mpemba effect in free-fermionic mixed states

Filiberto Ares, Vittorio Vitale+1 more|arXiv (Cornell University)|May 14, 2024

Quantum and electron transport phenomena4 citations

TL;DR

This paper investigates the quantum Mpemba effect (QMPE) in free-fermionic systems under non-unitary dynamics and mixed initial states, showing that QMPE persists under global gain-loss dissipation and local dephasing, though it is suppressed as mixedness increases. The key result is that QMPE survives in dissipative and finite-temperature settings, with the stationary state becoming independent of initial conditions in the presence of balanced dissipation.

ABSTRACT

Recently, a novel probe to study symmetry breaking, known as entanglement asymmetry, has emerged and has been utilized to explore how symmetry is dynamically restored following quantum quenches. Interestingly, it has been shown that, in certain scenarios, greater initial symmetry breaking leads to faster restoration, akin to a quantum Mpemba effect. This study focuses on investigating the effect of mixed initial states and non-unitary dynamics on symmetry restoration. The mixedness of a state can arise from different sources. We consider dephasing or dissipative processes affecting initial pure states or unitary dynamics of initially thermal states. In the former case, the stationary state after the quench is independent of the initial configuration, resembling the phenomenology of the classical Mpemba effect. Investigating the XY spin chain model, through a combination of analytical calculations and numerical simulations, we identify the conditions for the occurrence of the quantum Mpemba effect. It turns out that this phenomenon still occurs in the presence of dissipation or at finite temperature, even though it will be eventually suppressed as the state becomes more mixed.

Motivation & Objective

• To investigate how non-unitary dynamics and mixed initial states affect the quantum Mpemba effect (QMPE) in free-fermionic systems.
• To determine whether QMPE persists when initial states are mixed due to dephasing, gain-loss dissipation, or finite-temperature preparation.
• To analyze the role of entanglement asymmetry as a probe of symmetry restoration in non-equilibrium quantum dynamics.
• To examine the interplay between dissipation and initial state mixedness on the crossing time of entanglement asymmetry curves.
• To extend the quasiparticle picture to weakly dissipative hydrodynamic regimes in free-fermionic models.

Proposed method

• Analytical and numerical study of the XY spin chain under quantum quench dynamics with and without global gain-loss dissipation.
• Use of the entanglement asymmetry as a non-local observable to quantify U(1) symmetry breaking in subsystems.
• Derivation of equations of motion for two-point functions in free fermionic systems under local dephasing.
• Application of the replica trick to compute Rényi entanglement asymmetry for general index n, with focus on the replica limit.
• Extension of the quasiparticle picture to weakly dissipative regimes to explain exponential decay of entanglement asymmetry.
• Comparison of QMPE behavior in three scenarios: pure state with gain-loss, pure state with dephasing, and finite-temperature initial state.

Experimental results

Research questions

• RQ1 Does the quantum Mpemba effect persist when initial states are mixed due to dephasing or dissipation?
• RQ2 How does the presence of balanced gain-loss dissipation affect the conditions for QMPE compared to unitary dynamics?
• RQ3 What is the impact of local dephasing on the crossing time of entanglement asymmetry curves in the QMPE?
• RQ4 At what critical temperature does the QMPE disappear in a finite-temperature initial state?
• RQ5 How does the entanglement asymmetry evolve under non-unitary dynamics, and can the quasiparticle picture be extended to dissipative systems?

Key findings

• The quantum Mpemba effect persists under balanced global gain-loss dissipation, with the same conditions for occurrence as in the unitary case.
• Entanglement asymmetry decays exponentially in time under gain-loss dissipation, unlike the algebraic decay in unitary dynamics.
• Local dephasing suppresses the QMPE by shifting the crossing time of entanglement asymmetry curves toward later times, depending on the dephasing rate.
• The stationary state after a quench becomes independent of the initial state under balanced dissipation, analogous to the classical Mpemba effect.
• A critical finite temperature exists above which the QMPE disappears, with the critical temperature increasing with the Rényi index n.
• The charged moments in the replica formalism do not factorize in the presence of dissipation, preventing analytical computation of the entanglement asymmetry for general n.