Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces
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Quantum Physics arXiv:2601.18869 (quant-ph) [Submitted on 26 Jan 2026] Title:Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces Authors:Christopher David White, Michael Winer, Noam Bernstein View a PDF of the paper titled Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces, by Christopher David White and 2 other authors View PDF HTML (experimental) Abstract:Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\mathrm{av}} = \langle \psi | H | \psi\rangle$ display \textit{eigenstate condensation}: for $E_{\mathrm{av}}$ below a critical value $E_c$, they develop macroscopic overlap with the ground state. We study eigenstate condensation in systems with finite-dimensional Hilbert spaces. These systems display three phases: a ground-state phase, in which energy-constrained random states have macroscopic overlap with the ground state; a high-temperature phase, in which they have exponentially small overlap with each energy eigenstate; and an anti-ground-state phase, in which they have macroscopic overlap with the most highly excited state. In local spin systems the ground-state and anti-ground-state phases approach the middle of the spectrum as $1/[\text{system size}]$, but -- because the condensation phase transitions have exponential, rather than polynomial, finite-size scaling -- the crossover becomes exponentially sharp in system size and the high-temperature phase is best understood as an extended phase. Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2601.18869 [quant-ph] (or arXiv:2601.18869v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18869 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Christopher White [view email] [v1] Mon, 26 Jan 2026 19:00:01 UTC (2,942 KB) Full-text links: Access Paper: View a PDF of the paper titled Eigenstate condensation in quantum systems with finite-dimensional Hilbert spaces, by Christopher David White and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.dis-nn cond-mat.stat-mech cond-mat.str-el 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?)