# Generalized Crossover in Interacting Fermions within the Low-Energy Expansion

## TL;DR

This paper extends the BCS-BEC crossover theory for fermions to include arbitrary effective ranges, revealing new crossover phenomena and the limits of effective range expansion, with implications for ultracold gases and neutron matter.

## Contribution

It generalizes the BCS-BEC crossover to include effective range effects and identifies the breakdown region of the effective range expansion, providing a universal framework for low-energy fermionic systems.

## Key findings

- Identification of a new crossover driven by effective range $r_e$
- Discovery of the non-Hermitian regime where the effective range expansion fails
- Universal applicability to ultracold gases and neutron matter

## Abstract

We generalize the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover of two-component fermions, which is realized by tuning the $s$-wave scattering length $a$ between the fermions, to the case of an arbitrary effective range $r_{\rm e}$. By using the Nozi\`{e}res-Schmitt-Rink (NSR) approach, we show another crossover by changing $r_{\rm e}$ and present several similarities and differences between these two crossovers. Furthermore, the region ($r_{\rm e}>a/2$) where the effective range expansion breaks down and the Hamiltonian becomes non-Hermitian is found, being consistent with the Wigner's causality bound. Our results are universal for low-density interacting fermions with low-energy constants $a$ and $r_{\rm e}$ and are directly relevant to ultracold Fermi atomic gases as well as dilute neutron matter.