Stability of the two-dimensional Fermi polaron

TL;DR

This paper proves that the energy of a two-dimensional Fermi polaron system remains bounded below uniformly in the number of fermions when the impurity's mass exceeds a certain threshold, extending previous bounds and comparing to three-dimensional cases.

Contribution

It establishes a uniform lower bound on the energy of the 2D Fermi polaron system for a specific impurity mass, improving previous N-dependent bounds.

Findings

Energy is bounded below uniformly in N for impurity mass > 1.225 times fermion mass.

Provides a new lower bound that improves upon previous N-dependent bounds.

Complements similar results in three-dimensional Fermi polaron systems.

Abstract

A system composed of an ideal gas of N fermions interacting with an impurity particle in two space dimensions is considered. The interaction between impurity and fermions is given in terms of two-body point interactions whose strength is determined by the two-body binding energy, which is a free parameter of the model. If the mass of the impurity is 1.225 times larger than the mass of a fermion, it is shown that the energy is bounded below uniformly in the number N of fermions. This result improves previous, N-dependent lower bounds and it complements a recent, similar bound for the Fermi polaron in three space dimensions.