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arXiv:2409.06547 · Physical Review Letters

Imaginary-Time Mpemba Effect in Quantum Many-Body Systems

Wei-Xuan Chang, Shuai Yin, Shi‐Xin Zhang, Zixiang Li

Published Feb 12, 2026• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/dvrt-n2hq

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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.
Quantum imaginary-time evolution (QITE) is a fundamental framework for preparing ground and thermal states, yet its computational cost scales significantly with the evolution duration τττ. Reducing this duration is critical for practical quantum advantage. Here, we establish a unified theoretical framework for the Mpemba effect in QITE -- a counterintuitive phenomenon where a state initially farther from the ground state relaxes to it faster than one initially closer. We derive a remarkably simple necessary and sufficient condition for the occurrence of this effect, showing it is uniquely determined by the population ratios of excited states to the ground state. For practical state preparation, we introduce a rigorous sufficient condition for the finite-time Mpemba effect, ensuring the crossing occurs before reaching a prescribed proximity threshold. Furthermore, we unveil unique dynamical features, including a multiple-crossing phenomenon in multi-level systems and simultaneous intersections for collinear initial states. Our results provide criteria for identifying favorable initial states in QITE and offer deep insights into the speed limit of quantum state preparation.
We construct a controllable imaginary-time Mpemba effect in quantum spin systems using spatially modulated local rotations without changing initial bipartite entanglement spectra and correlation magnitudes. This feature unambiguously isolates the redistribution of spectral weights as the sole driver of the anomalous relaxation. Using the compact-boson description, we reveal that these twists act as precise mode selectors: higher-harmonic twists exclusively populate high-energy standing waves, structurally bypassing slow-decaying infrared modes to accelerate convergence. We derive exact analytical crossing times for these reversals and demonstrate that intentionally reintroducing the slow-mode population systematically delays the ITME. This exact mechanism is validated beyond the fixed-point theory via calculations on interacting XXZ chains and ladders. Furthermore, a twelve-qubit simulation of variational quantum imaginary-time evolution reproduces the reversals and their controlled delay, providing a concrete route to realize this protocol in realistic quantum circuits. Ultimately, these results provide a strictly controllable and exact starting point for realizing and investigating the imaginary-time Mpemba effect, establishing a foundational paradigm to harness anomalous non-equilibrium relaxation in quantum ground-state preparations.
Abstract Non-equilibrium dynamics have become a central research focus, exemplified by the counterintuitive Mpemba effect where initially hotter systems can cool faster than colder ones. Studied extensively in both classical and quantum regimes, this phenomenon reveals diverse and complex behaviors across different systems. This review provides a concise overview of the quantum Mpemba effect (QME), specifically emphasizing its connection to symmetry breaking and restoration in closed quantum many-body systems. We begin by outlining the classical Mpemba effect and its quantum counterparts, summarizing key findings. Subsequently, we introduce entanglement asymmetry and charge variance as key metrics for probing the QME from symmetry perspectives. Leveraging these tools, we analyze the early- and late-time dynamics of these quantities under Hamiltonian evolution and random unitary circuits. We conclude by discussing significant challenges and promising avenues for future research.
The Mpemba effect (MpE), where a far-from-equilibrium state of a system relaxes faster compared to a state closer to it, is a well-known counterintuitive phenomenon in classical and quantum systems. Various system-specific theories have been proposed to explain this anomalous behavior in driven systems, though the fundamental mechanism of MpE in undriven systems, where MpE was first observed, remains unresolved. This paper provides a generic model of MpE for a quantum spin-1/21/21/2 system following Markovian relaxation dynamics, regardless of system structure or environment. The key lies in the overlap of initial states with the fast relaxation mode; here, the constituents create a fast decay mode via interaction through the shared environment to show MpE, indicating that MpE happens due to the collective behavior of the system. I also show that a system with anisotropic relaxation naturally exhibits MpE, even without a shared environment among the particles.
Since its rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this Letter, we consider general non-Markovian open quantum systems and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Because of non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and nonequilibrium setups at weak, intermediate and strong coupling. Our Letter provides new insights into the rich physics underlying accelerated relaxation in quantum systems.
In classical settings, the Mpemba effect occurs when a hotter system cools faster than an initially colder one. In quantum systems, this effect can be reinterpreted exploiting the concept of symmetries, with the asymmetry of a subsystem playing the role of temperature. A quantum Mpemba effect arises when a more asymmetric state restores the symmetry faster than a less asymmetric one. Previous work mainly focuses on closed systems characterized by thermal equilibration and Hamiltonian symmetries. In this paper, we analyze the dynamics of asymmetry in an open quantum many-body system featuring symmetry breaking and uncover dynamical behavior that appears to be unique to these settings. In the symmetric phase, we demonstrate the existence of a quantum Mpemba effect, which emerges as a direct consequence of a non-monotonic evolution of the asymmetry. In the broken-symmetry phase, we analyze the imbalance between the system's ability to increase or to decrease its asymmetry. Our results extend the notion of quantum Mpemba effects to open quantum many-body systems exhibiting symmetry-breaking phase transitions and establish them as a platform for observing and controlling anomalous relaxation phenomena.