Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas

TL;DR

This study uses the complex Langevin method to analyze polarons in a one-dimensional attractive Fermi gas, demonstrating its effectiveness across various conditions and confirming results with the thermodynamic Bethe ansatz.

Contribution

It applies the complex Langevin approach to a 1D Fermi gas, showing its reliability and agreement with established solutions for polaron energies.

Findings

Complex Langevin works well across temperature and interaction ranges.

Polaron energy is insensitive to temperature and impurity concentration.

Results agree with thermodynamic Bethe ansatz at zero temperature.

Abstract

We investigate a polaronic excitation in a one-dimensional spin-1/2 Fermi gas with contact attractive interactions, using the complex Langevin method, which is a promising approach to evade a possible sign problem in quantum Monte Carlo simulations. We found that the complex Langevin method works correctly in a wide range of temperature, interaction strength, and population imbalance. The Fermi polaron energy extracted from the two-point imaginary Green's function is not sensitive to the temperature and the impurity concentration in the parameter region we considered. Our results show a good agreement with the solution of the thermodynamic Bethe ansatz at zero temperature.