Reference data for phase diagrams of triangular and hexagonal bosonic lattices

TL;DR

This paper provides precise reference data for phase boundaries in bosonic systems on triangular and hexagonal lattices, useful for experiments and theoretical models, and explores how these boundaries vary with particle filling.

Contribution

It introduces an accurate method for determining phase boundaries in the Bose-Hubbard model for various fillings on complex lattices, extending previous approaches.

Findings

Accurate phase boundary values for triangular and hexagonal lattices.

Critical hopping parameters scale with filling as predicted by mean-field theory.

Method applicable to arbitrary integer filling factors.

Abstract

We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g-dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.