Bose-Hubbard model with power-law hopping in one dimension
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arXiv
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| Format: | Preprint |
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2024
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| author | Gupta, Tanul Prokof'ev, Nikolay V. Pupillo, Guido |
| author_facet | Gupta, Tanul Prokof'ev, Nikolay V. Pupillo, Guido |
| contents | We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^α$ using exact large scale Quantum Monte-Carlo simulations. For all $1<α\leq 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in a way incompatible with the Berezinskii-Kosterlitz-Thouless (BKT) scenario, which is recovered for $α>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $α$ and from careful analysis of the spectrum. Large-scale simulations of the grand canonical phase diagram and of the decay of correlation functions demonstrate an overall behavior akin to higher dimensional systems with long-range order in the ground state for $α\leq 2$ and intermediate between one and higher dimensions for $2<α\leq 3$. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_01571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bose-Hubbard model with power-law hopping in one dimension Gupta, Tanul Prokof'ev, Nikolay V. Pupillo, Guido Quantum Gases Quantum Physics We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^α$ using exact large scale Quantum Monte-Carlo simulations. For all $1<α\leq 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in a way incompatible with the Berezinskii-Kosterlitz-Thouless (BKT) scenario, which is recovered for $α>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $α$ and from careful analysis of the spectrum. Large-scale simulations of the grand canonical phase diagram and of the decay of correlation functions demonstrate an overall behavior akin to higher dimensional systems with long-range order in the ground state for $α\leq 2$ and intermediate between one and higher dimensions for $2<α\leq 3$. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains. |
| title | Bose-Hubbard model with power-law hopping in one dimension |
| topic | Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2412.01571 |