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

Rukmani Bai; Soumik Bandyopadhyay; Sukla Pal; K. Suthar; D. Angom

doi:10.1007/978-981-13-9969-5_20

paper

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

arXiv:1911.08262 · doi:10.1007/978-981-13-9969-5_20

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 $α = 1/3$ . 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 $ν = 1/2, 1, 3/2, 2, 5/2$ with the cluster size $3 \times 2$ and $ν = 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3, 8/3$ 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 $ν$ , the competing superfluid (SF) state is the ground state and QH state is the metastable state.

6 pages, 4 figures. This is a pre-submission version of the manuscript. The published version is available online in "Quantum Collisions and Confinement of Atomic and Molecular Species, and Photons, Springer Proceedings in Physics 230, pp 211--221 (2019)". The final authenticated version is available online at : https://doi.org/10.1007/978-981-13-9969-5_20

Quantum Hall states for α=1/3 in optical lattices

Abstract

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