Quantum Mpemba effect in long-ranged U(1)-symmetric random circuits

TL;DR

This paper investigates the quantum Mpemba effect in long-range U(1)-symmetric random circuits, revealing how interaction range and initial charge bias influence the relaxation dynamics and the presence of the effect.

Contribution

It demonstrates the existence and absence of the quantum Mpemba effect in different initial states within long-range circuits and characterizes the scaling of the Mpemba time with subsystem size.

Findings

Quantum Mpemba effect occurs for ferromagnetic states at all ranges.

Absent for antiferromagnetic states regardless of range.

Mpemba time scales with subsystem size as $t_M \\sim N_A^z$, with $z=\\min(\\alpha-1,2)$.

Abstract

The Mpemba effect, where a state prepared farther from equilibrium relaxes faster to equilibrium than one prepared closer, has a quantum counterpart where relaxation is resolved by conserved charge. However, the fate of the quantum Mpemba effect in systems with long-range interactions remains an open question. Here, we study the quantum Mpemba effect in long-ranged, U(1)-symmetric random unitary circuits. Using annealed R\'enyi-2 entanglement asymmetry computed via replica tensor networks and exact diagonalization, we track the symmetry restoration from three types of tilted product states: ferromagnetic, antiferromagnetic, and ferromagnetic with a central domain wall. The quantum Mpemba effect is present for tilted ferromagnetic states at all interaction ranges, but absent for tilted antiferromagnetic states, and occurs for the domain-wall state only in effectively short-ranged circuits, where the Mpemba time $t_{\rm M}$ is found to scale with the subsystem size $N_A$ as $t_{\rm M}\!\sim\!N_{A}^{\,z}$, with the dynamical exponent $z=\min(\alpha-1,2)$. These results reveal how the quantum Mpemba effect is governed by the interplay between interaction range and initial-state charge bias in long-ranged chaotic systems.