# Two-dimensional Bose and Fermi gases beyond weak coupling

## TL;DR

This paper develops an analytic formalism based on the two-body S-matrix to study 2D Bose and Fermi gases with various interactions, accurately describing the BKT transition and critical parameters beyond weak coupling.

## Contribution

It introduces approximate analytic expressions valid beyond weak coupling for 2D Bose and Fermi gases, including BKT transition analysis and Tan's contact considerations.

## Key findings

- Correct logarithmic form of critical chemical potential and density for Bose gases
- Calculation of BKT critical temperature for fermions in BCS and BEC regimes
- Validation of the formalism beyond weak coupling regime

## Abstract

Using a formalism based on the two-body S-matrix we study two-dimensional Bose and Fermi gases with both attractive and repulsive interactions. Approximate analytic expressions, valid at weak coupling and beyond, are developed and applied to the Berezinskii-Kosterlitz-Thouless (BKT) transition. We successfully recover the correct logarithmic functional form of the critical chemical potential and density for the Bose gas. For fermions, the BKT critical temperature is calculated in BCS and BEC regimes through consideration of Tan's contact.