Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions

TL;DR

This paper derives universal relations for a two-dimensional spin-1/2 Fermi gas with contact interactions using a generalized selector function, simplifying the understanding of short-distance fermion behavior.

Contribution

It introduces an explicit form of a selector function in momentum space, enabling straightforward derivation of universal relations in 2D Fermi gases.

Findings

Derived universal relations for 2D Fermi gases with contact interactions.

Introduced a generalized selector function in momentum space.

Simplified derivation process akin to Tan's method for 3D gases.

Abstract

We present universal relations for a two-dimensional Fermi gas with pairwise contact interactions. The derivation of these relations is made possible by obtaining the explicit form of a generalized function -- selector -- in the momentum representation. The selector implements the short-distance boundary condition between two fermions in a straightforward manner, and leads to simple derivations of the universal relations, in the spirit of Tan's original method for the three-dimensional gas.