Slave particle approach to the finite temperature properties of ultracold Bose gases in optical lattices

TL;DR

This paper employs slave particle techniques to analyze the finite temperature behavior of ultracold Bose gases in optical lattices, revealing phase diagram features, excitation spectra, and stability differences between slave boson and slave fermion approaches.

Contribution

It introduces a comprehensive slave particle framework to study finite temperature effects in the Bose-Hubbard model, highlighting stability issues of the mean field states.

Findings

No qualitative difference between slave boson and slave fermion approaches for most quantities.

Slave boson mean field state is unstable, unlike the slave fermion approach.

The phase boundary is qualitatively correct but cannot capture second order phase transitions.

Abstract

By using slave particle (slave boson and slave fermion) technique on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitatively differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and can not describe the second order phase transition because the coefficient $a_4$ of the fourth order term is always negative in the free energy expansion.