Condensed Matter Theory

Dennis Hinrichs Perturbative calculation of critical exponents for the Bose–Hubbard model

Author(s): Dennis Hinrichs, Axel Pelster, Martin Holthaus

Perturbative calculation of critical exponents for the Bose-Hubbard model

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Article: Appl. Phys. B 113, 57 (2013), Springer-Verlag

Keywords: Bose-Hubbard model, high-order perturbation theory, Landau coefficients, critical exponents

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 a6 into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the twodimensional 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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URL: DOI:10.1007/s00340-013-5419-0

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