Mott phases and quantum phase transitions of extended Bose-Hubbard models in 2+1 dimensions

TL;DR

This paper reviews recent theoretical advances in understanding Mott phases and quantum phase transitions in extended Bose-Hubbard models on 2D lattices, emphasizing the dual vortex approach and lattice geometry effects.

Contribution

It highlights the role of lattice geometry in shaping Mott phases and quantum phase transitions, comparing dual vortex theory with quantum Monte Carlo results.

Findings

Lattice geometry critically influences Mott phase characteristics.

Dual vortex theory effectively describes quantum phase transitions.

Quantum Monte Carlo results support the dual vortex approach.

Abstract

We review the recent theoretical developments towards understanding the Mott phases and quantum phase transition of extended Bose-Hubbard models on lattices in two spatial dimensions . We focuss on the description of these systems using the dual vortex picture and point out the crucial role played by the geometry of underlying lattices in determining the nature of both the Mott phases and the quantum phase transitions. We also briefly compare the results of dual vortex theory with quantum Monte Carlo results.