Phase diagram of ultracold atoms on optical lattice: Comparative study to slave fermion and slave boson for Bose Hubbard modelPhase diagram of ultracold atoms in optical lattices: Comparative study of slave fermion and slave boson approaches to Bose-Hubbard model

TL;DR

This study compares slave fermion and slave boson methods for modeling ultracold Bose atoms in optical lattices, finding the slave fermion approach more accurate in predicting phase diagrams and critical temperatures.

Contribution

It demonstrates that the slave fermion approach provides a more accurate mean field description of the Bose-Hubbard model at finite temperatures.

Findings

Slave fermion approach better matches known limits.

Critical temperature predictions are more accurate with slave fermions.

Zero-temperature critical interaction strength aligns closer to direct calculations.

Abstract

We perform a comparative study of the finite temperature behavior of ultracold Bose atoms in optical lattices by the slave fermion and the slave boson approaches to the Bose Hubbard model. The phase diagram of the system is presented. Although both approaches are equivalent without approximations, the mean field theory based on the slave fermion technique is quantitatively more appropriate. Conceptually, the slave fermion approach automatically excludes the double occupancy of two identical fermions on the same lattice site. By comparing to known results in limiting cases, we find the slave fermion approach better than the slave boson approach. For example, in the non-interacting limit, the critical temperature of the superfluid-normal liquid transition calculated by the slave fermion approach is closer to the well-known ideal Bose gas result. At zero-temperature limit of the critical interaction strength from the slave fermion approach is also closer to that from the direct calculation using a zero-temperature mean field theory.