Boson-Gutzwiller Quantum liquids on a lattice

TL;DR

This paper explores self-bound liquid states in a one-dimensional Bose-Hubbard model with attractive two-body and repulsive three-body interactions, using the Gutzwiller approximation to analyze their properties and excitations.

Contribution

It demonstrates that the Gutzwiller mean-field approach can support and analyze quantum liquid states in a lattice Bose system with competing interactions.

Findings

Liquid states are supported by the Gutzwiller approximation.

A sharp transition to vacuum occurs at densities below equilibrium.

The excitation spectrum and speed of sound match thermodynamic predictions.

Abstract

We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive on-site two-body interactions, we include a three-body repulsive term such that the competition between these two forces allows the formation of self-bound liquid states. We investigate the properties of this system using the Gutzwiller approximation, showing that, indeed, this mean-field approach also supports liquid states. We find that for densities lower than the equilibrium density, the Gutzwiller method, and other mean-field approaches -- such as the Gross-Pitaevskii theory -- feature a sharp transition to the vacuum state. This, however, is avoided by considering local minima of the functional in the standard manner. We also study the excitation spectrum, and calculate the speed of sound, in full agreement with the usual expression obtained from the thermodynamic equation of state. We study their corresponding quantum droplets variationally and find that the results behave in accordance with the one-dimensional liquid drop model.