Phases and collective modes of hardcore Bose-Fermi mixture in an optical lattice

TL;DR

This paper explores the complex phase diagram of a hardcore Bose-Fermi mixture in an optical lattice, revealing four distinct phases, their transitions, and collective excitations using mean-field theory.

Contribution

It provides a comprehensive mean-field analysis of the phase diagram and collective modes of a Bose-Fermi mixture with specific interactions in an optical lattice.

Findings

Identifies four possible phases including supersolid, Mott, and metallic states.

Shows most phase transitions are first order, except the supersolid-Mott transition which is continuous.

Determines the dynamical critical exponent for the supersolid-Mott insulator transition.

Abstract

We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless Bosons and spin-polarized Fermions with nearest neighbor intra-species interaction and on-site inter-species repulsion in an optical lattice at half-filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are a) supersolid Bosons coexisting with Fermions in the Mott state, b) Mott state of Bosons coexisting with Fermions in a metallic or charge-density wave state, c) a metallic Fermionic state coexisting with superfluid phase of Bosons, and d) Mott insulating state of Fermions and Bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transition between these phases are generically first order with the exception of that between the supersolid and the Mott states which is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.