The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

TL;DR

This paper investigates the phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interactions using DMRG, identifying phase boundaries, the nature of phase transitions, and properties of the superfluid phase.

Contribution

It provides a detailed phase diagram including charge density wave, superfluid, and Bose-glass phases, with new insights into the effects of nearest-neighbor interactions and disorder.

Findings

Identified a direct transition between charge density wave and superfluid phases.

Found no supersolid or normal phases in the model.

Calculated ac-conductivity and superfluid stiffness in different interaction regimes.

Abstract

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.