Effective interaction in an unbalanced Fermion mixture

TL;DR

This paper studies a one-dimensional imbalanced Fermi mixture with delta interaction, calculating properties like dispersion, polaron mass, and effective interactions between minority Fermions, using a determinant-based reformulation of Bethe ansatz wave functions.

Contribution

It introduces a determinant-based reformulation of Bethe ansatz wave functions to analyze effective interactions in an imbalanced Fermi mixture.

Findings

Calculated dispersion relations and polaron masses for minority Fermions.

Derived an explicit expression for the effective interaction potential.

Analyzed density-density correlators in the system.

Abstract

A one dimensional Fermi mixture with delta--interaction is investigated in the limit of extreme imbalance. In particular we consider the cases of only one or two minority Fermions which interact with the Fermi-sea of the majority Fermions. We calculate dispersion relation and polaron mass for the minority Fermions as well as equal time density-density correlators. Within a cluster expansion we derive an expression for the effective interaction potential between minority Fermions. For our calculations we use a reformulation of the exact wave functions, originally obtained by Yang and Gaudin by a nested Bethe ansatz, in terms of determinants.