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Torus geometry eigenfunctions of an interacting multi-Landau-level Hamiltonian

Journal Article · · Physical Review. B
 [1];  [2];  [3]
  1. Indian Institute of Science Education and Research, Pune (India); OSTI
  2. University of Leeds (United Kingdom); Pennsylvania State Univ., University Park, PA (United States)
  3. Indian Institute of Science Education and Research, Pune (India)
+ Show Author Affiliations
A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al., Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact many-body eigenfunctions on the disk not just for quasiholes but for all charged and neutral excitations of the entire Jain sequence filling fractions. We extend this to geometries without full rotational symmetry, namely, the torus and cylinder geometries, and present their spectra. Exact diagonalization of the interaction on the torus produces the low-energy spectra at filling fraction v = n/(2⁢pn + 1) that is identical, up to a topological (2⁢pn + 1)-fold multiplicity, to that of the integer quantum Hall spectra at v = n, for the incompressible state as well as all excitations. While the ansatz eigenfunctions in the disk geometry cannot be generalized to closed geometries such as torus or sphere, we show how to extend them to cylinder geometry. Meanwhile, we show eigenfunctions for charged excitations at filling fractions between 1/3 and 2/5 can be written on the torus and the spherical geometries.
Research Organization:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Organization:
Government of India; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0005042
OSTI ID:
2419672
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 19 Vol. 107; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Composite fermions
Fractional quantum Hall effect
Materials Science
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Quantum Hall effect