Candidate parent Hamiltonian for the 3/7 fractional quantum Hall state

ORAL

Abstract

The Trugman-Kivelson (TK) interaction [1] has been long known as a parent Hamiltonian for the 1/3 Laughlin wave function. When the lowest two Landau levels (LLs) are assumed to be degenerate, this interaction also produces the unprojected composite-fermion wave function at n/(2n+1) with n=2 as a unique zero-mode [2]. However, this approach encounters difficulties at n=3 (i.e. 3/7 filling) because numerous zero modes are generated by the TK interaction within the lowest three LLs. Here, we introduce a local three-body interaction to single out the 3/7 wave function from the zero-mode subspace. Our extensive diagonalization studies on finite systems provide strong support for this proposal [4].

[1] S. A. Trugman and S. Kivelson, Phys. Rev. B 31, 5280 (1985).

[2] J. K. Jain, Phys. Rev. B 41, 7653 (1990); E. H. Rezayi and A. H. MacDonald, Phys. Rev. B 44, 8395 (1991).

[3] S. Bandyopadhyay, L. Chen, M. T. Ahari, G. Ortiz, Z. Nussinov, and A. Seidel, Phys. Rev. B 98, 161118(R) (2018).

[4] K. Kudo, A. Sharma, G. J. Sreejith, and J. K. Jain, Phys. Rev. B 108, 085130 (2023).

* K.K. acknowledges financial support from JSPS Overseas Research Fellowships and JST CREST, Grant No. JPMJCR18T2. A.S. and J.K.J. acknowledge financial support from the U.S. National Science Foundation under Grant No. DMR-2037990.

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Publication: K. Kudo, A. Sharma, G. J. Sreejith, and J. K. Jain, Phys. Rev. B 108, 085130 (2023).

Presenters

  • Koji Kudo

    Kyushu University

Authors

  • Koji Kudo

    Kyushu University

  • Anirban Sharma

    Pennsylvania State University

  • Sreejith Ganesh Jaya

    Indian Institute of Science Education and Research, Pune, IISER Pune

  • Jainendra K Jain

    Pennsylvania State University