The quantum Mpemba effect in symmetric random Clifford circuits

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.