Effective Action Approach for Quantum Phase Transitions in Bosonic Lattices

TL;DR

This paper develops an effective action framework for analyzing quantum phase transitions in lattice Bose systems, providing detailed expressions for phase boundaries, order parameters, and excitation spectra, and compares favorably with mean-field theory.

Contribution

It introduces a novel effective action approach for lattice Bose systems at finite temperature, extending standard field theory methods to derive phase boundaries and excitation spectra.

Findings

Accurate phase boundary expressions for Mott insulator-superfluid transition.

Effective action predictions surpass mean-field results inside the superfluid phase.

Derived excitation spectra considering both longitudinal and transverse order parameter variations.

Abstract

Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, we then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced in the standard way, and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator - superfluid phase boundary to first order in the tunneling, the predictions of our effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.