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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.03029 |
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| _version_ | 1866912411539210240 |
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| author | Preuß, Meret |
| author_facet | Preuß, Meret |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems Preuß, Meret Quantum Gases 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. |
| title | Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2506.03029 |