Repulsive interactions in quantum Hall systems as a pairing problem
23 págs.; 4 figs.; 5 tabs. PACS number(s): 73.43.Cd, 02.30.Ik, 74.20.Rp A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within...
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ftcsic:oai:digital.csic.es:10261/140570 2024-02-11T10:05:21+01:00 Repulsive interactions in quantum Hall systems as a pairing problem Ortiz, G. Nussinov, Z. Dukelsky, Jorge Seidel, A. Max Planck Institute for Astrophysics Ministerio de Ciencia e Innovación (España) National Science Foundation (US) 2013-10-08 http://hdl.handle.net/10261/140570 https://doi.org/10.1103/PhysRevB.88.165303 https://doi.org/10.13039/501100004837 https://doi.org/10.13039/100000001 unknown American Physical Society Publisher's version https://doi.org/10.1103/PhysRevB.88.165303 Sí doi:10.1103/PhysRevB.88.165303 issn: 1098-0121 Physical Review B - Condensed Matter and Materials Physics 88: 165303 (2013) http://hdl.handle.net/10261/140570 http://dx.doi.org/10.13039/501100004837 http://dx.doi.org/10.13039/100000001 open artículo http://purl.org/coar/resource_type/c_6501 2013 ftcsic https://doi.org/10.1103/PhysRevB.88.16530310.13039/50110000483710.13039/100000001 2024-01-16T10:18:55Z 23 págs.; 4 figs.; 5 tabs. PACS number(s): 73.43.Cd, 02.30.Ik, 74.20.Rp A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px+ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px+ip y)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a >squeezing principle> that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) >incompressible filling factors> for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional ... Article in Journal/Newspaper IPY Digital.CSIC (Spanish National Research Council) Physical Review B 88 16 |
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23 págs.; 4 figs.; 5 tabs. PACS number(s): 73.43.Cd, 02.30.Ik, 74.20.Rp A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px+ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px+ip y)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a >squeezing principle> that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) >incompressible filling factors> for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional ... |
author2 |
Max Planck Institute for Astrophysics Ministerio de Ciencia e Innovación (España) National Science Foundation (US) |
format |
Article in Journal/Newspaper |
author |
Ortiz, G. Nussinov, Z. Dukelsky, Jorge Seidel, A. |
spellingShingle |
Ortiz, G. Nussinov, Z. Dukelsky, Jorge Seidel, A. Repulsive interactions in quantum Hall systems as a pairing problem |
author_facet |
Ortiz, G. Nussinov, Z. Dukelsky, Jorge Seidel, A. |
author_sort |
Ortiz, G. |
title |
Repulsive interactions in quantum Hall systems as a pairing problem |
title_short |
Repulsive interactions in quantum Hall systems as a pairing problem |
title_full |
Repulsive interactions in quantum Hall systems as a pairing problem |
title_fullStr |
Repulsive interactions in quantum Hall systems as a pairing problem |
title_full_unstemmed |
Repulsive interactions in quantum Hall systems as a pairing problem |
title_sort |
repulsive interactions in quantum hall systems as a pairing problem |
publisher |
American Physical Society |
publishDate |
2013 |
url |
http://hdl.handle.net/10261/140570 https://doi.org/10.1103/PhysRevB.88.165303 https://doi.org/10.13039/501100004837 https://doi.org/10.13039/100000001 |
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IPY |
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IPY |
op_relation |
Publisher's version https://doi.org/10.1103/PhysRevB.88.165303 Sí doi:10.1103/PhysRevB.88.165303 issn: 1098-0121 Physical Review B - Condensed Matter and Materials Physics 88: 165303 (2013) http://hdl.handle.net/10261/140570 http://dx.doi.org/10.13039/501100004837 http://dx.doi.org/10.13039/100000001 |
op_rights |
open |
op_doi |
https://doi.org/10.1103/PhysRevB.88.16530310.13039/50110000483710.13039/100000001 |
container_title |
Physical Review B |
container_volume |
88 |
container_issue |
16 |
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1790602319910404096 |