Eigenstate Thermalization for Local versus Translationally Invariant Observables
Summarize this article with:
Quantum Physics arXiv:2602.09087 (quant-ph) [Submitted on 9 Feb 2026] Title:Eigenstate Thermalization for Local versus Translationally Invariant Observables Authors:Rohit Patil, Marcos Rigol View a PDF of the paper titled Eigenstate Thermalization for Local versus Translationally Invariant Observables, by Rohit Patil and Marcos Rigol View PDF HTML (experimental) Abstract:Local observables and their translationally invariant counterparts are generally thought as providing the same predictions for experimental measurements. This is used in the context of their expectation values, which are indeed the same in clean systems (up to finite-size effects), but also in the context of their correlation functions, which need not be the same. We examine this intuition from the perspective of the eigenstate thermalization hypothesis. Specifically, we explore the diagonal matrix elements and the spectral functions of local and translationally invariant observables in the spin-1 tilted field Ising chain with periodic and open boundary conditions. We discuss in which ways those observables are different and in which contexts they can be thought as being the same. Furthermore, we unveil a novel form of off-diagonal eigenstate thermalization in translationally invariant systems that applies to pairs of energy eigenstates with different quasimomenta. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2602.09087 [quant-ph] (or arXiv:2602.09087v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.09087 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rohit Patil [view email] [v1] Mon, 9 Feb 2026 19:00:00 UTC (3,502 KB) Full-text links: Access Paper: View a PDF of the paper titled Eigenstate Thermalization for Local versus Translationally Invariant Observables, by Rohit Patil and Marcos RigolView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)