Excitation spectra and rank tomography of linear matrix product tangent spaces

Abstract:We formulate a tangent-space method for algebraic varieties of matrix product states (MPS) to study excitation spectra of non-uniform quantum many-body systems with open boundary conditions. We further introduce a rank tomography of the MPS tangent space, which characterizes its expressivity in terms of particle-sector rank profiles of the underlying MPS variety. Using the Bose--Hubbard model as a benchmark, we illustrate that the method reproduces low-lying excitations and captures finite-size precursors of the Mott-insulator to superfluid transition.

15 double-sided pages, 6 figures. v2: Updated reference to completed work; otherwise unchanged

Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

arXiv:2607.05269 [cond-mat.quant-gas]

(or arXiv:2607.05269v2 [cond-mat.quant-gas] for this version)

https://doi.org/10.48550/arXiv.2607.05269 Focus to learn more arXiv-issued DOI via DataCite

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