Quantum Hall states for $\alpha = 1/3$ in optical lattices

TL;DR

This paper investigates quantum Hall states in optical lattices with flux $rac{1}{3}$ using Bose-Hubbard model and cluster Gutzwiller mean-field theory, revealing state sensitivities to cluster size and metastability of QH states.

Contribution

It applies cluster Gutzwiller mean-field theory to identify quantum Hall states at specific fillings for flux $rac{1}{3}$, highlighting the impact of cluster size on state geometry.

Findings

QH states found at specific fillings depending on cluster size

QH states are metastable, with superfluid states as ground states

State geometry varies with cluster size

Abstract

We examine the quantum Hall (QH) states of the optical lattices with square geometry using Bose-Hubbard model (BHM) in presence of artificial gauge field. In particular, we focus on the QH states for the flux value of $\alpha = 1/3$. For this, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes of $3\times 2$ and $3\times 3$. We obtain QH states at fillings $\nu = 1/2, 1, 3/2, 2, 5/2$ with the cluster size $3\times 2$ and $\nu = 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3, 8/3$ with $3\times 3$ cluster. Our results show that the geometry of the QH states are sensitive to the cluster sizes. For all the values of $\nu$, the competing superfluid (SF) state is the ground state and QH state is the metastable state.