Competing phases, phase separation and co-existence in the extended one-dimensional bosonic Hubbard model

TL;DR

This paper maps the phase diagram of a one-dimensional bosonic Hubbard model with contact and near neighbor interactions, revealing the conditions for the Haldane insulator, supersolid phases, and phase separation.

Contribution

It provides a detailed phase diagram showing the existence of the Haldane insulator only at density 1 and the widespread presence of the supersolid phase.

Findings

Haldane insulator exists only at density 1

Supersolid phase exists over a wide parameter range

Phase separation occurs at fixed integer density

Abstract

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact ($U$) and near neighbor ($V$) interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime ($U$, $V$ and $\mu$) where this phase exists and how it competes with other phases such as the supersolid (SS) phase, is incompletely understood. We use the Stochastic Green Function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $\rho=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings) and displays power law decay in the one body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.