Finite-Element Matrix Product States for Continuum Models in One Dimension

• URL: http://arxiv.org/abs/2606.14873v1
• Date: Fri, 12 Jun 2026 18:20:21 GMT
• Title: Finite-Element Matrix Product States for Continuum Models in One Dimension
• Abstract summary: We present a matrix product state framework for simulating one-dimensional quantum many-body systems in the continuum.<n>We show that the resulting many-body overlap operator can be efficiently encoded as a matrix product operator for sufficiently localized orbitals.<n>We employ a first-order finite-element expansion to study the ground state properties of the Lieb-Liniger gas in the presence of inhomogeneities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a matrix product state framework for simulating one-dimensional quantum many-body systems in the continuum using non-orthogonal single-particle basis sets. By mapping the physical problem to an auxiliary computational space, we show that the resulting many-body overlap operator can be efficiently encoded as a matrix product operator for sufficiently localized orbitals, thereby generalizing a construction that first appeared in [arXiv:2405.10285]. This construction recasts the variational ground-state search into a generalized eigenvalue problem, which can be solved using a generalized density matrix renormalization group algorithm. As a primary application, we employ a first-order finite-element expansion to study the ground state properties of the Lieb-Liniger gas in the presence of inhomogeneities. This approach also provides a natural setting for exactly refining the lattice, thereby enabling multigrid optimization strategies for matrix product states.

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