Perturbative calculation of critical exponents for the Bose-Hubbard model

作者：Hinrichs Dennis^*; Pelster Axel; Holthaus Martin

来源：Applied Physics B: Lasers and Optics , 2013, 113(1): 57-67.

DOI：10.1007/s00340-013-5419-0

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.

• 出版日期2013-10