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arXiv · 1912.00679

Quantum critical properties of Bose-Hubbard models

Sören Sanders·Martin Holthaus
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Abstract

The Mott insulator-to-superfluid transition exhibited by the Bose-Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing a numerical approach based on a combination of high-order perturbation theory and hypergeometric analytic continuation we investigate how quantum critical properties manifest themselves in computational practice. We consider two-dimensional triangular lattices and three-dimensional cubic lattices for comparison, providing accurate parametrizations of the phase boundaries at the tips of the respective first lobes. In particular, we lend strong support to a recently suggested inequality which bounds the divergence exponent of the one-particle correlation function in terms of that of the two-particle correlation function, and which sharpens to an equality if and only if a system becomes critical.

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Sören Sanders, Martin Holthaus. 2019-12-02. Quantum critical properties of Bose-Hubbard models. https://doi.org/10.1088/1751-8121/ab2153

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