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Title: Geometric construction of quantum hall clustering Hamiltonians

In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
Authors:
 [1] ;  [2] ;  [3]
  1. Stanford Univ., Stanford, CA (United States); Institute of High Performance Computing, Singapore (Singapore)
  2. Univ. of Leeds, Leeds (United Kingdom); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Institute for Quantum Computing, Waterloo, ON (Canada)
  3. Univ. of Wurzburg, Wurzburg (Germany)
Publication Date:
OSTI Identifier:
1223341
Grant/Contract Number:
SC0002140
Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Volume: 5; Journal Issue: 4; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Research Org:
Princeton Univ., NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; condensed matter physics