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.
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.
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.
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 tM is found to scale with the subsystem size NA as tM∼NAz, with the dynamical exponent 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.
Abstract The entanglement asymmetry is an observable independent tool to investigate the relaxation of quantum many-body systems through the restoration of an initially broken symmetry of the dynamics. In this paper we use this to investigate the effects of interactions on quantum relaxation in a paradigmatic integrable model. Specifically, we study the dynamical restoration of the U(1) symmetry corresponding to rotations about the z-axis in the XXZ model quenched from a tilted ferromagnetic state. We find two distinct patterns of behaviour depending upon the interaction regime of the model. In the gapless regime, at roots of unity, we find that the symmetry restoration is predominantly carried out by bound states of spinons of maximal length. The velocity of these bound states is suppressed as the anisotropy is decreased toward the isotropic point leading to slower symmetry restoration. By varying the initial tilt angle, one sees that symmetry restoration is slower for an initially smaller tilt angle, signifying the presence of the quantum Mpemba effect. In the gapped regime, however, spin transport for non maximally tilted states is dominated by smaller bound states with longer bound states becoming frozen. This leads to much longer time scales for restoration compared to the gapless regime. In addition, the quantum Mpemba effect is absent in the gapped regime.
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.
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) 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.