# Thermal field theory of bosonic gases with finite-range effective interaction

## TL;DR

This paper develops an effective field theory for dilute ultracold Bose gases incorporating finite-range interactions, deriving analytical results for the equation of state and stability conditions at zero and finite temperatures.

## Contribution

It introduces a beyond-mean-field analytical framework accounting for finite-range effects, extending previous zero-range models and aligning with Monte Carlo simulations.

## Key findings

- Finite-range effects stabilize the Bose gas against quantum fluctuations.
- A positive effective range above a critical value removes thermodynamic instability.
- Results agree with recent Monte Carlo calculations for hard-sphere bosons.

## Abstract

We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical partition function we derive beyond-mean-field analytical results which depend on both scattering length and effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.