Energy and contact of the one-dimensional Fermi polaron at zero and finite temperature

TL;DR

This paper employs the T-matrix approach to analyze the one-dimensional Fermi polaron, providing accurate ground state energies and contact values at zero and finite temperatures, including an exact zero-temperature contact expression.

Contribution

It introduces an exact zero-temperature contact expression and extends the T-matrix method to finite temperatures for one-dimensional Fermi polarons.

Findings

Excellent agreement with exact and numerical methods at zero temperature

Derived an exact expression for the contact parameter at zero temperature

Analyzed temperature dependence of energies and contact parameter

Abstract

We use the T-matrix approach for studying highly polarized homogeneous Fermi gases in one dimension with repulsive or attractive contact interactions. Using this approach, we compute ground state energies and values for the contact parameter that show excellent agreement with exact and other numerical methods at zero temperature, even in the strongly interacting regime. Furthermore, we derive an exact expression for the value of the contact parameter in one dimension at zero temperature. The model is then extended and used for studying the temperature dependence of ground state energies and the contact parameter.