Mean-field approximations for short-range four-body interactions at ν=35

Bartosz Kuśmierz, Arkadiusz Wójs, and G. J. Sreejith
Phys. Rev. B 99, 235141 – Published 20 June 2019

Abstract

Trial wave functions such as the Moore-Read and Read-Rezayi states, which minimize short-range multibody interactions, are candidate states for describing the fractional quantum Hall effects at filling factors ν=1/2 and 2/5 in the second Landau level. These trial wave functions are unique zero-energy states of three-body and four-body interaction Hamiltonians, respectively, but they are not close to the ground states of the Coulomb interaction. Previous studies using extensive parameter scans have found optimal two-body interactions on the sphere that produce states close to these. Here we focus on short-ranged four-body interaction and study two mean-field approximations that reduce the four-body interactions to two-body interactions on the sphere by replacing composite operators with their incompressible ground-state expectation values. We present the results for pseudopotentials of these approximate interactions. A comparison of finite system spectra on the sphere of the four-body and the approximate interactions at filling fraction ν=3/5 shows that these approximations produce good effective descriptions of the low-energy structure of the four-body interaction Hamiltonian. The approach also independently reproduces the optimal two-body interaction inferred from parameter scans. We also show that for n=3, but not for n=4, the mean-field approximations of the n-body interaction are equivalent to particle-hole symmetrization of the interaction. Within the system sizes accessible, analysis of the spectrum of the mean-field two-body Hamiltonian on the torus was inconclusive, and indicates a competing anisotropic state in the system.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
8 More
  • Received 26 February 2019
  • Revised 23 May 2019

DOI:https://doi.org/10.1103/PhysRevB.99.235141

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bartosz Kuśmierz1,2, Arkadiusz Wójs1, and G. J. Sreejith2

  • 1Department of Theoretical Physics, Wroclaw University of Science and Technology, Poland
  • 2IISER Pune, Dr. Homi Bhabha Road, Pune 411008, India

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 23 — 15 June 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×