Renormalization group approach to spinor Bose-Fermi mixtures in a shallow optical lattice

TL;DR

This paper uses a renormalization group approach to analyze how spinor bosons in a shallow optical lattice influence fermionic superfluidity and Fermi surface separation, revealing potential broken-symmetry states.

Contribution

It introduces a novel RG analysis of spinor Bose-Fermi mixtures, showing how bosons induce Fermi surface separation and affect superfluid instabilities.

Findings

Bosons can cause Fermi surface separation of spin-up and spin-down fermions.

Identification of parameter regimes for superfluid instabilities.

Prediction of possible broken-symmetry ground states.

Abstract

We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the bosons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible broken-symmetry ground states at low temperatures and weak interactions.