Generalized effective-potential Landau theory for a tunable state-dependent hexagonal optical lattice

TL;DR

This paper develops a generalized effective-potential Landau theory to analyze ground-state phase diagrams of ultracold bosons in a tunable, state-dependent hexagonal optical lattice, providing insights into Mott lobe behaviors.

Contribution

It introduces a new analytical approach that accounts for site-offset tunability and third-order corrections, aligning well with previous numerical methods.

Findings

Analytical phase diagrams match cluster Gutzwiller results.

Identifies why Mott lobes expand unexpectedly with increasing tunneling.

Provides a deeper understanding of state-dependent lattice effects.

Abstract

We analytically study the ground-state phase diagrams of ultracold bosons with various values of the effective magnetic quantum number $m$ in a state-dependent hexagonal optical lattice by using the generalized effective-potential Landau theory, where the site-offset energy between the two triangular sublattice A and B is tunable. Our analytical calculations of third-order corrections are in reasonably good agreement with the previous cluster Gutzwiller calculations. Furthermore, we reveal the reason why the regions of the Mott lobes $(n,n)$ in phase diagrams for $m=0.02$ are unexpectedly expanded with increasing $J/U$ in deep lattice.