Thermalization and irreversibility of an isolated quantum system

• URL: http://arxiv.org/abs/2503.04152v1
• Date: Thu, 06 Mar 2025 07:01:29 GMT
• Title: Thermalization and irreversibility of an isolated quantum system
• Authors: Xue-Yi Guo,
• Abstract summary: We show that erasure of spreaded nonequilibrium state information by local operations can be used to explain the irreversibility and thermalization of many-body systems.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The irreversibility and thermalization of many-body systems can be attributed to the erasure of spreaded nonequilibrium 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 nonequilibrium 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.

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