# Effective expression of the Lee-Huang-Yang energy functional for heteronuclear mixtures

## TL;DR

This paper derives an accurate approximation of the Lee-Huang-Yang energy functional for heteronuclear Bose mixtures at mean-field collapse, showing it closely resembles the homonuclear case with specific parameter conditions.

## Contribution

It introduces a simplified, accurate expression for the LHY energy functional in heteronuclear mixtures, extending the homonuclear form with two fitting parameters.

## Key findings

- The approximated LHY functional matches the homonuclear form under permutation invariance.
- Parameter values for heteronuclear mixtures are identical to the homonuclear case.
- Quantitative analysis of deviations from the exact LHY functional.

## Abstract

We consider a homogeneous heteronuclear Bose mixture with contact interactions at the mean-field collapse, i.e. with interspecies attraction equal to the mean geometrical intraspecies repulsion. We show that the Lee-Huang-Yang (LHY) energy functional is accurately approximated by an expression that has the same functional form as in the homonuclear case. The approximated energy functional is characterized by two exponents, which can be treated as fitting parameters. We demonstrate that the values of these parameters which preserve the invariance under permutation of the two atomic species are exactly those of the homonuclear case. Deviations from the exact expression of LHY energy functional are discussed quantitatively and a specific application is described.