A non-degeneracy theorem for interacting fermions in one dimension

[2503.18440] A non-degeneracy theorem for interacting fermions in one dimension Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Spectral Theory arXiv:2503.18440 (math) [Submitted on 24 Mar 2025 ( v1 ), last revised 23 Mar 2026 (this version, v2)] Title: A non-degeneracy theorem for interacting fermions in one dimension Authors: Thiago Carvalho Corso View a PDF of the paper titled A non-degeneracy theorem for interacting fermions in one dimension, by Thiago Carvalho Corso View PDF HTML (experimental) Abstract: In this paper, we show that the ground-state of many-body Schrödinger operators for electrons in one dimension is non-degenerate. More precisely, we consider Schrödinger operators of the form $H_N(v,w) = -\Delta + \sum_{i\neq j}^N w(x_i,x_j) + \sum_{j=1}^N v(x_i)$ acting on $\wedge^N \mathrm{L}^2([0,1])$, where the external and interaction potentials $v$ and $w$ belong to a large class of distributions. In this setting, we show that the ground-state of the system with Fermi statistics and local boundary conditions is non-degenerate and does not vanish on a set of positive measure. In the case of periodic and anti-periodic (or more general non-local) boundary conditions, we show that the same result holds whenever the number of particles is odd and even, respectively. This non-degeneracy result seems to be new even for regular potentials $v$ and $w$. As an immediate application of this result, we prove eigenvalue inequalities and the strong unique continuation property for eigenfunctions of the single-particle one-dimensional operators $h(v) = -\Delta +v$. In addition, we prove strict inequalities between the lowest eigenvalues of different self-adjoint realizations of $H_N(v,w)$. Comments: Revised version to appear in Annales Henri Poincaré Subjects: Spectral Theory (math.SP) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) MSC classes: Primary: 81Q10 Secondary: 35J10, 81V74 Cite as: arXiv:2503.18440 [math.SP] (or arXiv:2503.18440v2 [math.SP] for this version) https://doi.org/10.48550/arXiv.2503.18440 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s00023-026-01693-0 Focus to learn more DOI(s) linking to related resources Submission history From: Thiago Carvalho Corso [ view email ] [v1] Mon, 24 Mar 2025 08:41:37 UTC (105 KB) [v2] Mon, 23 Mar 2026 14:55:55 UTC (103 KB) Full-text links: Access Paper: View a PDF of the paper titled A non-degeneracy theorem for interacting fermions in one dimension, by Thiago Carvalho Corso View PDF HTML (experimental) TeX Source view license Current browse context: math.SP < prev | next > new | recent | 2025-03 Change to browse by: math math-ph math.MP quant-ph References & Citations INSPIRE HEP NASA ADS Google 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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