Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics

The quantum Pontus-Mpemba effect (QPME) is a counterintuitive phenomenon wherein a quantum system relaxes more rapidly through a two-step evolution protocol than through direct evolution under a symmetric Hamiltonian alone. In this protocol, the system first evolves under a symmetry-breaking Hamiltonian and then switches to a symmetric one. We demonstrate that QPME occurs under both real-time and imaginary-time dynamics with respect to $U(1)$-symmetry. Using tilted ferromagnetic initial states, we demonstrate that a transient asymmetric evolution significantly accelerates thermalization or convergence to the ground state for both real-time and imaginary-time evolutions, respectively. The effect is pronounced for small tilt angles, while larger tilts or antiferromagnetic initial states suppress it. Numerical evidence across different system sizes confirms the robustness of QPME, demonstrating its stability in the thermodynamic limit. This work extends the framework of nonequilibrium quantum phenomena to incorporate active state preparation, with direct implications for the implementation of quantum simulation.