Competition of superfluidity and density waves in one-dimensional Bose-Fermi mixtures

TL;DR

This paper investigates the interplay between superfluidity and density waves in one-dimensional Bose-Fermi mixtures, deriving response function exponents and analyzing how interactions influence superfluid and density-wave fluctuations.

Contribution

It provides an exact analysis of response function exponents in 1D Bose-Fermi mixtures, highlighting how interactions affect superfluid and density wave behaviors.

Findings

Superfluid fluctuations are enhanced by density-density interactions.

Superfluid exponent varies non-monotonically with velocity ratio under certain conditions.

Density-wave and fermionic superfluidity exponents are monotonic functions of velocity ratio.

Abstract

We study a mixture of one-dimensional bosons and spinless fermions at incommensurate filling using phenomenological bosonization and Green's functions techniques. We derive the relation between the parameters of the microscopic Hamiltonian and macroscopic observables. Galilean invariance results in extra constraints for the current current interactions. We obtain the exact exponents for the various response functions, and show that superfluid fluctuations are enhanced by the effective boson-fermion density-density interaction and suppressed by the effective boson-fermion current-current interaction. In the case of a bosonized model with purely density-density interaction, when the effective boson-fermion density-density interaction is weak enough, the superfluid exponent of the bosons has a non-monotonous variation with the ratio of the fermion velocity to the boson velocity. By contrast, density-wave exponent and the exponent for fermionic superfluidity are monotonous functions of the velocity ratio.