# Flow equations for cold Bose gases

## TL;DR

This paper develops flow equations for cold Bose gases to accurately compute ground state energies, using a self-consistent truncation scheme and benchmarking against the Lieb-Liniger model.

## Contribution

It introduces a novel flow equation approach with a self-consistent truncation for three-body operators in cold Bose gases, enabling precise energy calculations.

## Key findings

- Good agreement with Lieb-Liniger model for weak/moderate interactions
- Effective estimation of truncation errors
- Method applicable to general N-body systems

## Abstract

We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a general $N$-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb-Liniger model and find good agreement for weak and moderate interaction strengths.