Excitation spectra and rank tomography of linear matrix product tangent spaces

[2607.05269] Excitation spectra and rank tomography of finite MPS tangent spaces Skip to main content Search Submit Donate Log in Condensed Matter > Quantum Gases arXiv:2607.05269 (cond-mat) [Submitted on 6 Jul 2026 ( v1 ), last revised 7 Oct 2026 (this version, v3)] Title: Excitation spectra and rank tomography of finite MPS tangent spaces Authors: Otto T.P. Schmidt , Iacopo Carusotto View PDF HTML (experimental) Abstract: We formulate the matrix product state (MPS) tangent-space excitation construction for finite, non-uniform systems with open boundary conditions, using the smooth full-rank stratum of the MPS variety as the variational manifold. The resulting linear tangent ansatz yields a projected-Hamiltonian eigenproblem for approximating excitation spectra. We further introduce a rank tomography that characterizes the particle-sector expressivity of the MPS tangent space. For number-conserving systems, we resolve the Schmidt ranks of reference states by particle number and derive an explicit relation between the resulting rank profile and the dimensions of the tangent-space sectors. This allows sector completeness and parametric deficiency to be determined directly from the reference state, without explicitly constructing a tangent basis, and provides a direct diagnostic of the sectorwise expressivity of the MPS excitation ansatz. We benchmark the finite-system construction on Bose--Hubbard chains against exact diagonalization, finding accurate low-lying excitation branches while identifying sector-dependent limitations of the linear tangent ansatz. Comments: 19 double-sided pages, 6 figures. v2: Updated reference to completed work; otherwise unchanged. v3: Updated manuscript for publication Subjects: Quantum Gases (cond-mat.quant-gas) ; Quantum Physics (quant-ph) Cite as: arXiv:2607.05269 [cond-mat.quant-gas] (or arXiv:2607.05269v3 [cond-mat.quant-gas] for this version) https://doi.org/10.48550/arXiv.2607.05269 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Otto Theodor Primus Schmidt [ view email ] [v1] Mon, 6 Jul 2026 16:19:20 UTC (357 KB) [v2] Thu, 27 Aug 2026 07:32:34 UTC (357 KB) [v3] Wed, 7 Oct 2026 14:38:17 UTC (272 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.quant-gas < prev | next > new | recent | 2026-07 Change to browse by: cond-mat quant-ph References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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)

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