Eigenstate thermalization for local versus translationally invariant observables

Abstract:Local observables and their translationally invariant counterparts are generally thought to provide the same predictions for experiments. While this equivalence holds for expectation values in clean systems (up to finite-size effects), it is often assumed to extend to correlation functions, where it need not hold. We examine this assumption from the perspective of the eigenstate thermalization hypothesis. Specifically, we explore the spectral functions of local and translationally invariant observables in the spin-1 tilted-field Ising chain with periodic and open boundary conditions. We identify the contexts in which these observables and boundary conditions differ and those in which they are interchangeable. We unveil an off-diagonal eigenstate thermalization in translationally invariant systems for matrix elements between energy eigenstates with different quasimomenta.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2602.09087 [quant-ph]

(or arXiv:2602.09087v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.09087 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B 114, L171105 (2026)

https://doi.org/10.1103/fw73-69y5 Focus to learn more DOI(s) linking to related resources

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