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arXiv:2510.12875 · Physical review. B./Physical review. B

Tunable quantum Mpemba effect in long-range interacting systems

Andrew Hallam, Matthew Yusuf, Aashish A. Clerk, Ivar Martin, Zlatko Papić

Published Aug 3, 2026• 1 citation
arXivHTMLPDF

Abstract

Symmetry plays a fundamental role in many-body systems, both in and out of equilibrium. The quantum Mpemba effect (QME)—a phenomenon where systems initially farther from equilibrium can thermalize faster—can be understood in terms of how rapidly a symmetry, broken by initial conditions, is dynamically restored. In this work, we study the QME in a one-dimensional spin-1/2 XYZ model with power-law decaying interactions in the presence of a magnetic field. In the prethermal regime generated by large field strengths, the system develops a continuous U(1) symmetry, enabling the QME to emerge. However, due to the Hohenberg-Mermin-Wagner theorem, the QME can only arise when interactions are sufficiently short-ranged. This leads to an interplay between the external field, interaction range, and dynamical symmetry restoration. We systematically explore this interplay and analyze the dependence of the QME on the effective temperature set by the initial state. Our results demonstrate the tunability of the QME via long-range interactions, which can be probed in experimental platforms of trapped ions, polar molecules, and NV centers.

DOI
10.1103/kvth-my1s

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Symmetry plays a fundamental role in many-body systems, both in and out of equilibrium. The quantum Mpemba effect (QME)—a phenomenon where systems initially farther from equilibrium can thermalize faster—can be understood in terms of how rapidly a symmetry, broken by initial conditions, is dynamically restored. In this work, we study the QME in a one-dimensional spin-1/2 XYZ model with power-law decaying interactions in the presence of a magnetic field. In the prethermal regime generated by large field strengths, the system develops a continuous U(1) symmetry, enabling the QME to emerge. However, due to the Hohenberg-Mermin-Wagner theorem, the QME can only arise when interactions are sufficiently short-ranged. This leads to an interplay between the external field, interaction range, and dynamical symmetry restoration. We systematically explore this interplay and analyze the dependence of the QME on the effective temperature set by the initial state. Our results demonstrate the tunability of the QME via long-range interactions, which can be probed in experimental platforms of trapped ions, polar molecules, and NV centers.
One of the manifestations of the quantum Mpemba effect (QME) is that a tilted ferromagnet exhibits faster restoration of the spin-rotational symmetry after a quantum quench when starting from a larger tilt angle. This phenomenon has recently been observed experimentally in an ion trap that simulates a long-range spin chain. However, the underlying mechanism of the QME in the presence of long-range interactions remains unclear. Using the time-dependent spin-wave theory, we investigate the dynamical restoration of the spin-rotational symmetry and the QME in generic long-range spin systems. We show that quantum fluctuations of the magnetization drive the restoration of symmetry by melting the initial ferromagnetic order and are responsible for the QME. We find that this effect occurs across a wide parameter range in long-range systems, in contrast to its absence in some short-range counterparts.
The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.
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 Rényi-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 tMt_{\rm M}tM​ is found to scale with the subsystem size NAN_ANA​ as tM ⁣∼ ⁣NA zt_{\rm M}\!\sim\!N_{A}^{\,z}tM​∼NAz​, with the dynamical exponent z=min⁡(α−1,2)z=\min(α-1,2)z=min(α−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.
The quantum Mpemba effect (QME) describes the counterintuitive phenomenon where a system initially further from equilibrium relaxes faster than one closer to it. Specifically, the QME associated with symmetry restoration has been extensively investigated across integrable, ergodic, and disordered localized systems. However, its fate in disorder-free ergodicity-breaking settings, such as the Stark many-body localized (Stark-MBL) phase, remains an open question. Here, we explore the dynamics of local U(1) symmetry restoration in a Stark-MBL XXZ spin-12 chain, using the Rényi-2 entanglement asymmetry (EA) as a probe. Using an analytical operator-string expansion supported by numerical simulations, we demonstrate that the QME transitions from an initial-state-dependent anomaly in the ergodic phase to a universal feature in the Stark-MBL regime. Moreover, the Mpemba time scales exponentially with the subsystem size, even in the absence of global transport, and is governed by high-order off-resonant processes. We attribute this robust inversion to a Stark-induced hierarchy of relaxation channels that fundamentally constrains the effective Hilbert space dimension. The findings pave the way for utilizing tunable potentials to engineer and control anomalous relaxation timescales in quantum technologies without reliance on quenched disorder.
Understanding relaxation in isolated quantum many-body systems remains a central challenge. Recently, the quantum Mpemba effect (QME), a counterintuitive relaxation phenomenon, has attracted considerable attention and has been extensively studied in systems with global symmetries. Here, we study the QME in gauge theories with massive local gauge symmetries. In the lattice Schwinger model, we demonstrate that the gauge structure of the reduced density matrix of a subsystem is entirely determined by the initial state and remain unchanged during the time evolution. We then investigate whether gauge symmetry can be dynamically restored following a symmetric quench. Analytical and numerical results show that when the Maxwell term is zero, gauge symmetry restoration fails due to the emergence of a peculiar conservation law. However, for any finite Maxwell term, subsystem gauge symmetry is restored in the thermodynamic limit. Based on these results, we systematically construct a families of initial states exhibiting the QME. We further explore the QME in the quantum link model-a truncated lattice Schwinger model, which has been realized in experiments. Moreover, we propose an experimentally accessible order parameter that correctly captures the QME. Our work demonstrates the generality of the quantum Mpemba effect even in the local gauge symmetries, and are directly relevant to ongoing quantum simulation experiments of gauge theories.
The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in U(1)U(1)U(1) symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.