Competing Supersolid and Haldane Insulator phases in the extended one-dimensional bosonic Hubbard model

TL;DR

This paper investigates the phase diagram of the one-dimensional bosonic Hubbard model, revealing the coexistence and competition of supersolid and Haldane insulator phases using advanced numerical methods.

Contribution

It provides the first detailed numerical analysis of the conditions under which Haldane insulator and supersolid phases occur and coexist in this model.

Findings

Haldane insulator exists only at the tip of the unit filling CDW lobe.

A stable supersolid phase exists over a wide parameter range.

Charge density waves, superfluid, supersolid, and Haldane insulator phases are identified.

Abstract

The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the Stochastic Green Function (SGF) quantum Monte Carlo (QMC) and the Density Matrix Renormalization Group (DMRG), we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves (CDW), superfluid (SF), supersolid (SS) and the recently identified Haldane insulating (HI) phases. We show that the HI exists only at the tip of the unit filling CDW lobe and that there is a stable SS phase over a very wide range of parameters.