Geometric construction of quantum hall clustering Hamiltonians
In this study, many fractional quantum Hall wave functions are known to be unique highestdensity 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 nonAbelian states, such as the ReadRezayi series (in particular, the MooreRead and ReadRezayi Z _{3} states) and more exotic nonunitary (HaldaneRezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated manybody 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 nonAbelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Stanford Univ., Stanford, CA (United States); Institute of High Performance Computing, Singapore (Singapore)
 Univ. of Leeds, Leeds (United Kingdom); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Institute for Quantum Computing, Waterloo, ON (Canada)
 Univ. of Wurzburg, Wurzburg (Germany)
 Publication Date:
 Grant/Contract Number:
 SC0002140
 Type:
 Published Article
 Journal Name:
 Physical Review. X
 Additional Journal Information:
 Journal Volume: 5; Journal Issue: 4; Journal ID: ISSN 21603308
 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
 OSTI Identifier:
 1223341
 Alternate Identifier(s):
 OSTI ID: 1239300
Lee, Ching Hua, Papić, Zlatko, and Thomale, Ronny. Geometric construction of quantum hall clustering Hamiltonians. United States: N. p.,
Web. doi:10.1103/PhysRevX.5.041003.
Lee, Ching Hua, Papić, Zlatko, & Thomale, Ronny. Geometric construction of quantum hall clustering Hamiltonians. United States. doi:10.1103/PhysRevX.5.041003.
Lee, Ching Hua, Papić, Zlatko, and Thomale, Ronny. 2015.
"Geometric construction of quantum hall clustering Hamiltonians". United States.
doi:10.1103/PhysRevX.5.041003.
@article{osti_1223341,
title = {Geometric construction of quantum hall clustering Hamiltonians},
author = {Lee, Ching Hua and Papić, Zlatko and Thomale, Ronny},
abstractNote = {In this study, many fractional quantum Hall wave functions are known to be unique highestdensity 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 nonAbelian states, such as the ReadRezayi series (in particular, the MooreRead and ReadRezayi Z3 states) and more exotic nonunitary (HaldaneRezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated manybody 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 nonAbelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.},
doi = {10.1103/PhysRevX.5.041003},
journal = {Physical Review. X},
number = 4,
volume = 5,
place = {United States},
year = {2015},
month = {10}
}