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Quantum Hall States for \(\alpha = 1/3\) in Optical Lattices

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Quantum Collisions and Confinement of Atomic and Molecular Species, and Photons

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 230))

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 is 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.

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Authors and Affiliations

  1. Physical Research Laboratory, Ahmedabad, 380009, Gujarat, India

    Rukmani Bai, Soumik Bandyopadhyay, Sukla Pal, K. Suthar & D.  Angom

  2. Indian Institute of Technology Gandhinagar, Gandhinagar, 382355, Gujarat, India

    Rukmani Bai & Soumik Bandyopadhyay

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  1. Rukmani Bai
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Correspondence to D.  Angom .

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Editors and Affiliations

  1. Indian Institute of Technology Tirupati, Tirupati, India

    P. C. Deshmukh

  2. Raman Research Institute, Bangalore, India

    E. Krishnakumar

  3. Helmholtz Institute Jena, Jena, Germany

    Stephan Fritzsche

  4. Tata Institute of Fundamental Research, Mumbai, India

    M. Krishnamurthy

  5. Indian Institute of Technology Kharagpur, Kharagpur, India

    Sonjoy Majumder

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Bai, R., Bandyopadhyay, S., Pal, S., Suthar, K., Angom, D. (2019). Quantum Hall States for \(\alpha = 1/3\) in Optical Lattices. In: Deshmukh, P., Krishnakumar, E., Fritzsche, S., Krishnamurthy, M., Majumder, S. (eds) Quantum Collisions and Confinement of Atomic and Molecular Species, and Photons. Springer Proceedings in Physics, vol 230. Springer, Singapore. https://doi.org/10.1007/978-981-13-9969-5_20

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  • DOI: https://doi.org/10.1007/978-981-13-9969-5_20

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