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arXiv:1912.00679 · Journal of Physics A Mathematical and Theoretical

Quantum critical properties of Bose–Hubbard models

Sören Sanders, Martin Holthaus

Published May 13, 2019• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8121/ab2153

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