Metastable quantum phase transitions in a periodic one-dimensional Bose gas: II. Many-body theory

TL;DR

This paper establishes a precise connection between quantum solitons and yrast states in a 1D Bose gas, extending the understanding of metastable quantum phase transitions from weak to strong interactions using exact methods.

Contribution

It clarifies the physical meaning of Lieb's type II excitations and demonstrates the extension of metastable phase transitions into the strongly-interacting regime.

Findings

Quantum solitons are identified as yrast states.

Metastable quantum phase transitions extend into strong interactions.

Exact diagonalization and Bethe ansatz methods are employed.

Abstract

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions clearly with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean field analysis of the weakly-interacting Lieb-Liniger Hamiltonian [Phys. Rev. A {\bf 79}, 063616 (2009)] extends into the medium- to strongly-interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.