Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions

TL;DR

This paper investigates the quantum phase transition in one-dimensional attractive Bose-Einstein condensates, revealing discrepancies between mean-field predictions and exact quantum results, especially regarding the energy gap at the critical point.

Contribution

It provides an exact diagonalization analysis showing the presence of an energy gap at the transition, challenging mean-field theory predictions.

Findings

Mean-field theory predicts a gapless transition with a cusp.

Exact diagonalization finds a finite energy gap at the critical point.

Quantum fluctuations smear the mean-field singularity.

Abstract

Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform condensate and a bright soliton, and a gapless singular cusp in the Bogoliubov excitation spectrum at the critical point. However, the exact diagonalization reveals the presence of an energy gap at the critical point, where the singularity is smeared by quantum fluctuations.