Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems

• URL: http://arxiv.org/abs/2304.04213v1
• Date: Sun, 9 Apr 2023 11:02:48 GMT
• Title: Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems
• Abstract summary: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with mean field interaction. This mathematically verifies the observation made in [L.Santos and M.Rigol, Phys.Rev.E 82, 031130] that ETH may hold for systems with additional translation symmetries for a naturally restricted class of observables.
• Score: 0.5505634045241288
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with mean field interaction. This mathematically verifies the observation made in [L.Santos and M.Rigol, Phys.Rev.E 82, 031130 (2010, https://journals.aps.org/pre/abstract/10.1103/PhysRevE.82.031130)] that ETH may hold for systems with additional translation symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interactions.

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