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arXiv:2609.17988

The quantum Mpemba effect in symmetric random Clifford circuits

Shion Yamashika, Filiberto Ares, Pasquale Calabrese

cond-mat.stat-mechquant-phSubmitted Sep 16, 2026• Announced Sep 17, 2026• 0 citations
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Abstract

The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved $\mathrm{U}(1)$ charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.

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8+10 pages, 3+1 figures

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The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved U(1)\mathrm{U}(1)U(1) charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.
Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to nonsymmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and Z_{2} symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.
The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.
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 essence of the Mpemba effect is that nonequilibrium systems may relax faster the further they are from their equilibrium configuration. In the quantum realm, this phenomenon arises in closed systems dynamics and is witnessed by features of symmetry and entanglement. Here, we study the quantum Mpemba effect in charge-preserving random circuits, combining extensive numerical simulations and analytical arguments. We show that the more asymmetric certain classes of initial states (tilted ferromagnets) are, the faster they restore symmetry and reach the grand-canonical ensemble. Conversely, other classes of states (tilted antiferromagnets) do not show the Mpemba effect. We provide a simple and general mechanism underlying the effect, based on the spreading of nonconserved operators in terms of conserved densities. Grounded only in locality, unitarity, and symmetry, our analysis clarifies the emergence of Mpemba physics in chaotic quantum systems.
A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed Rényi-2 entanglement asymmetry up to L=128L=128L=128, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.
Abstract The Mpemba effect refers to a counterintuitive phenomenon whereby a system initially prepared further from equilibrium may relax faster than one prepared closer to equilibrium. While extensively studied in classical nonequilibrium physics, its extension to isolated quantum systems only started in the last few years. In this contribution we review recent progress on the quantum Mpemba effect in closed many-body systems, emphasizing the role of reduced density matrix, entanglement and symmetry restoration. We discuss why and how the entanglement asymmetry provides a natural and experimentally accessible framework to characterize Mpemba-like behavior in unitary quantum evolution.