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arXiv · 2506.03029

Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems

Meret Preuß
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Abstract

In this paper, higher-order perturbation theory is applied and tailored to one-dimensional ring-shaped Bose-Hubbard systems. Spectral and geometrical properties are used to structurally simplify the contributions and reduce computational effort without sacrificing accuracy. For this, a guide for the computation of the individual perturbational orders up to order nine is provided, alongside a both system-specific and parametrization-dependent convergence criterion. The simplification scheme described is found to be applicable to a wider class of Bose-Hubbard systems with different lattice geometries. An exemplary validation of these findings is included in the form of explicit calculations of ground state energies of the three-site Bose-Hubbard system with repulsive on-site interactions. These calculations are successfully checked against numerical computations of exact diagonalization results.

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Meret Preuß. 2025-06-03. Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems. https://doi.org/10.1088/1402-4896%2Faddfb0

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