How the effective boson-boson interaction works in Bose-Fermi mixtures in periodic geometries

TL;DR

This paper investigates how boson-boson interactions in Bose-Fermi mixtures within 2D optical lattices depend on temperature, providing analytical expressions for phase transition temperatures and phase diagrams.

Contribution

It introduces an analytical approach to determine temperature-dependent effective interactions and phase transition points in Bose-Fermi mixtures.

Findings

Derived a relation for boson-boson effective interaction as a function of temperature.

Provided analytical formulas for supersolid and phase separation transition temperatures.

Generated phase diagrams illustrating stability regions of different phases.

Abstract

We study mixtures of spinless bosons and not spin-polarized fermions loaded in two dimensional optical lattices. We approach the problem of the ground state stability within the framework of the linear response theory; by the mean of an iterative procedure, we are able to obtain a relation for the dependence of boson-boson effective interaction on the absolute temperature of the sample. Proceeding from such a formula, we write down analyitical expressions for Supersolid (SS) and Phase Separation (PS) transition temperatures, and plot the phase diagrams.