Thermalization and irreversibility of an isolated quantum system

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 of $\hat{O}_i(t_i)$, where $\hat{O_i}$ is a local operator, $\hat{O_i}(t_i) = e^{i\hat{H}t_i} \hat{O_i} e^{-i\hat{H}t_i}$, $\hat{H}$ is the system Hamiltonian, $t_i$ can take positive, negative, or zero values, and the sequence is arranged according to the subscript $i$. We numerically demonstrate the information erasure of initial non-equilibrium quantum states through such sequence in a one-dimensional Hubbard model. During this process, the system's entanglement entropy increases monotonically toward a stable value. By incorporating this information erasure mechanism into an isolated system, our numerical simulations reveal that in this completely isolated system, a thermalization process emerges.