Ab initio lattice results for Fermi polarons in two dimensions

TL;DR

This paper introduces a new Monte Carlo algorithm to study Fermi polarons in two dimensions, providing the first non-perturbative results on polaron energy and impurity correlations, revealing a crossover from quasiparticle to molecular states.

Contribution

The paper presents the impurity lattice Monte Carlo method, enabling efficient non-perturbative calculations of Fermi polarons in two dimensions for the first time.

Findings

First non-perturbative 2D polaron energy calculations.

Evidence of a smooth crossover from quasiparticle to molecular state.

Benchmark results in 3D agree with existing literature.

Abstract

We investigate the attractive Fermi polaron problem in two dimensions using non-perturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully non-perturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of interaction strength.