Quantum phase transitions of ultra-cold Bose system in non-rectangular optical lattices

TL;DR

This paper analytically studies quantum phase transitions between Mott-insulator and Superfluid phases in ultracold bosons within various non-rectangular optical lattices, confirming results with numerical data.

Contribution

It provides an analytical approach to determine phase boundaries in triangular, hexagonal, and Kagomé lattices, extending understanding of quantum phase transitions in complex lattice geometries.

Findings

Analytical phase boundaries match numerical results

Effective potential method applied to non-rectangular lattices

Phase diagrams for different filling factors derived

Abstract

In this paper, we investigate systematically the Mott-insulator-Superfluid quantum phase transitions for ultracold scalar bosons in triangular, hexagonal, as well as Kagom\'e optical lattices. With the help of field-theoretical effective potential, by treating the hopping term in Bose-Hubbard model as perturbation, we calculate the phase boundaries analytically for different integer filling factors. Our analytical results are in good agreement with recent numerical results.