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arXiv · 1401.0680

Perturbative calculation of critical exponents for the Bose-Hubbard model

Dennis Hinrichs·Axel Pelster·Martin Holthaus
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Abstract

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose-Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient $a_6$ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose-Hubbard model, deviate by less than $1\%$ from the best known estimates computed so far for the three-dimensional $XY$ universality class.

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Dennis Hinrichs, Axel Pelster, Martin Holthaus. 2014-01-03. Perturbative calculation of critical exponents for the Bose-Hubbard model. https://doi.org/10.1007/s00340-013-5419-0

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