Pairing and density-wave phases in Boson-Fermion mixtures at fixed filling

TL;DR

This paper investigates a two-dimensional boson-fermion mixture on an optical lattice, revealing various ordered phases such as antiferromagnetism, superconductivity, and charge density waves driven by tunable interactions, using advanced renormalization group analysis.

Contribution

It introduces a detailed phase diagram analysis of boson-fermion mixtures at fixed filling, incorporating full frequency dependence in the renormalization group approach.

Findings

Identification of phase transitions driven by interaction tuning.

Quantitative estimates of energy gaps for different ordered phases.

Demonstration of the impact of retardation effects on phase stability.

Abstract

We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two hyperfine (isospin) states and the bosons have Bose-Einstein condensed (BEC). The coupling between the fermionic atoms and the bosonic fluctuations of the BEC has similarities with the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site (half-filling). We find that tuning of the lattice parameters and interaction strengths (for fermion-fermion, fermion-boson and boson-boson interactions) drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity or a charge density wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account by keeping the frequency dependence of the interaction vertices and self-energies. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.