Conserved quantities enable the quantum Mpemba effect in weakly open systems

TL;DR

This paper investigates the quantum Mpemba effect in weakly open many-body systems, revealing that the presence of multiple conserved quantities is essential for the effect to occur, supported by numerical evidence.

Contribution

It identifies the role of conserved quantities in enabling the quantum Mpemba effect and demonstrates this through numerical simulations using tensor networks and free-fermion methods.

Findings

The quantum Mpemba effect occurs only when the Hamiltonian has multiple conserved quantities.

Dissipation constrains dynamics within a single-parameter manifold when energy is the only conserved quantity.

Multiple conserved quantities lead to multi-dimensional dynamics in generalized Gibbs ensembles.

Abstract

Observation of the quantum Mpemba effect has spurred much interest in its enabling conditions and its relation to the classical counterpart. Here, we consider weakly open many-body quantum systems initialized in different thermal states and examine when the initially farther state relaxes to the (non-equilibrium) steady state faster. We claim that the number of conserved quantities in the unitary part plays a crucial role: the Mpemba effect is possible only when the Hamiltonian commutes with other extensive operators or is integrable. The reason lies in the dynamical evolution happening in spaces of different dimensions. When energy is the only approximately conserved quantity, dissipation pushes the dynamics within a single-parameter manifold of different thermal states. In contrast, for Hamiltonians with several conserved quantities, the dynamics drift in the multi-dimensional space of generalized Gibbs ensembles, whose distance to the steady state is less trivial. We provide numerical results for large system sizes using tensor networks and free-fermion techniques, thereby supporting our claim.