Tunable quantum Mpemba effect in long-range interacting systems

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.