Thermalization and irreversibility of an isolated quantum system

Abstract: The irreversibility and thermalization of many-body systems can be attributed to the erasure of spread non-equilibrium state information by local operations. This thermalization mechanism can be demonstrated by the sequence $[\hat{O}^\dagger \hat{O}(t)]^N$, where $\hat{O}$ is a local operator, $\hat{O}(t) = e^{i\hat{H}t} \hat{O} e^{-i\hat{H}t}$, $\hat{H}$ is the system Hamiltonian, and $N$ denotes the number of repetitions. We begin by preparing a non-equilibrium initial state with an inhomogeneous particle number distribution in a one-dimensional Hubbard model. As particles propagate and interact within the lattice, the system evolves into a highly entangled quantum state, where the entanglement entropy satisfies a volume law, yet the information of the initial state remains well preserved. The local operator $\hat{O}$ erases part of the information in the entangled state, altering the interference of the system wavefunction and the disentangling process during time-reversed evolution. Repeatedly applying $\hat{O}^\dagger \hat{O}(t)$ leads to a monotonic increase in the entanglement entropy until it saturates at a steady value. By incorporating this information erasure mechanism into the one-dimensional Hubbard model, our numerical simulations demonstrate that in a completely isolated system, a thermalization process emerges. Finally, we discuss the feasibility of implementing related quantum simulation experiments on superconducting quantum processors.