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

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.

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

arXiv:2606.14873 [quant-ph]

(or arXiv:2606.14873v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.14873 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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