Related papers: Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect

Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect

URL: http://arxiv.org/abs/2509.01608v1
Date: Mon, 01 Sep 2025 16:38:09 GMT
Title: Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
Authors: Gilles Parez, Vincenzo Alba,
Abstract summary: We investigate the out-of-equilibrium dynamics after a quantum quench of the reduced fidelities between the states of a subregion $A$.<n>We denote these fidelities as the reduced Loschmidt echo (RLE) and the final-state fidelity (FSF)<n>We show that the FSF provides a valuable tool to detect the so-called quantum Mpemba effect.
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License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We investigate the out-of-equilibrium dynamics after a quantum quench of the reduced fidelities between the states of a subregion $A$ at different times. Precisely, we consider the fidelity between the time-dependent state of $A$ and its initial value, as well as with the state at infinite time. We denote these fidelities as the reduced Loschmidt echo (RLE) and the final-state fidelity (FSF), respectively. If region $A$ is the full systems, the RLE coincide with the standard Loschmidt echo. We focus on quenches from Gaussian states in several instances of the XY spin chain. In the hydrodynamic limit of long times and large sizes of $A$, with their ratio fixed, the reduced fidelities admit a quasiparticle picture interpretation. Interestingly, for some quenches in the hydrodynamic regime the RLE features a complicated structure with an infinite sequence of nested lightcones, corresponding to quasiparticles with arbitrary large group velocities. This leads to a ''staircase'' of cusp-like singularities in the time-derivative of the fidelity. At the sub-hydrodynamic regime for some quenches the RLE exhibits cusp-like singularities, similar to the so-called dynamical quantum phase transitions (DQPT). We conjecture a criterion for the occurrence of the DQPT and for the ''critical'' times at which the singularities occur. Finally, we discuss the hydrodynamic limit of the FSF. In particular, we show that it provides a valuable tool to detect the so-called quantum Mpemba effect.

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