Imaginary-Time Mpemba Effect in Quantum Many-Body Systems

Various exotic phenomena emerge in nonequilibrium quantum many-body systems. The Mpemba effect, denoting the situation where a hot system freezes faster than a colder one, is a counterintuitive nonequilibrium phenomenon that has attracted enduring interest for more than half a century. In this Letter, we unveil a novel phenomenon of the Mpemba effect in the imaginary-time relaxation dynamics in quantum many-body systems, termed as the imaginary-time Mpemba effect (ITME). We propose a mechanism for the ITME rooted in the initial state's eigenbasis expansion, and we demonstrate its emergence in representative quantum lattice models. Using sign-free quantum Monte Carlo (QMC) simulations, we unequivocally establish the existence of the ITME across diverse interacting quantum systems. Crucially, given the widespread use of imaginary-time dynamics for ground-state calculations, the discovery of the ITME potentially provides a new pathway to accelerate quantum many-body simulations, particularly for QMC methods hindered by the sign problem.