Bose-Hubbard model with power-law hopping in one dimension

• URL: http://arxiv.org/abs/2412.01571v2
• Date: Wed, 08 Jan 2025 11:43:25 GMT
• Title: Bose-Hubbard model with power-law hopping in one dimension
• Authors: Tanul Gupta, Nikolay V. Prokof'ev, Guido Pupillo,
• Abstract summary: We investigate the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/ralpha$. For all $1alphaleq 3$ the quantum phase transition from a superfluid and a Mott at unit filling is found to be continuous and scale invariant.
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• Abstract: We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^\alpha$ using exact large scale Quantum Monte-Carlo simulations. For all $1<\alpha\leq 3$ 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 $\alpha>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $\alpha$ 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 $\alpha \leq 2$ and intermediate between one and higher dimensions for $2<\alpha \leq 3$. 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.

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