Perturbative calculation of critical exponents for the Bose-Hubbard model

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.

11 pages, 9 figures

References in corpus (11)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Experimental demonstration of single-site addressability in a two-dimensional optical lattice
• Critical Behavior of a Trapped Interacting Bose Gas
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Quantum Phase Diagram of Bosons in Optical Lattices
• Bose-Hubbard phase diagram with arbitrary integer filling
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• Effective Action Approach for Quantum Phase Transitions in Bosonic Lattices
• Process chain approach to high-order perturbation calculus for quantum lattice models
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• High-order symbolic strong-coupling expansion for the Bose-Hubbard model
• Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory
• Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems