Imaginary-time Mpemba effect in quantum many-body systems

TL;DR

This paper discovers a novel imaginary-time Mpemba effect in quantum many-body systems, where higher-energy states relax faster than lower-energy ones, potentially improving quantum simulation efficiency.

Contribution

It introduces the imaginary-time Mpemba effect in quantum systems and demonstrates its occurrence through quantum Monte Carlo simulations, linking it to low-energy excitations.

Findings

Higher-energy initial states relax faster in imaginary-time dynamics.

The effect is observed across different quantum models.

ITME could accelerate quantum many-body computations.

Abstract

Various exotic phenomena emerge in non-equilibrium quantum many-body systems. The Mpemba effect, denoting the situation where a hot system freezes faster than the colder one, is a counterintuitive non-equilibrium phenomenon that has attracted enduring interest for more than half a century. In this Letter, we report a novel phenomenon of the Mpemba effect in the imaginary-time relaxation dynamics in quantum many-body systems, dubbed as imaginary-time Mpemba effect (ITME). Through numerically exact quantum Monte-Carlo (QMC) simulation, we unambiguously demonstrate that in different classes of interacting quantum models, the initial states with higher energy are relaxed faster than lower-energy initial states in the process of imaginary-time relaxation. The emergence of ITME is intimately associated with the low-energy excitations in quantum many-body systems. More crucially, since imaginary-time dynamics is broadly applied in numerical simulation on the quantum many-body ground states, the discovery of ITME potentially provides a new pathway to expedite the quantum many-body computation, particularly for QMC involving the sign problem.