Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory
Abstract
In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-{1/2} semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-{1/2} semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2){sub {kappa}=1} Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2){sub {kappa}=1} Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs.
- Authors:
-
- Los Alamos National Lab., NM (United States) Landau Inst. for Theoretical Physics of the Academy of Science of the USSR, Moscow (USSR)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; USDOE, Washington, DC (United States)
- OSTI Identifier:
- 5924084
- Report Number(s):
- LA-UR-91-3717; CONF-9108184-1
Journal ID: ISSN 0217--9792; ON: DE92003871
- DOE Contract Number:
- W-7405-ENG-36
- Resource Type:
- Conference
- Resource Relation:
- Journal Volume: 06; Journal Issue: 05n06; Conference: Adriatico conference on strongly correlated electrons, Trieste (Italy), Aug 1991
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GINZBURG-LANDAU THEORY; HALL EFFECT; QUANTUM MECHANICS; ELECTRON CORRELATION; LAGRANGIAN FUNCTION; SPIN; SU-2 GROUPS; WAVE FUNCTIONS; ANGULAR MOMENTUM; CORRELATIONS; FUNCTIONS; LIE GROUPS; MECHANICS; PARTICLE PROPERTIES; SU GROUPS; SYMMETRY GROUPS; 665411* - Basic Superconductivity Studies- (1992-); 661100 - Classical & Quantum Mechanics- (1992-)
Citation Formats
Balatsky, A. Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory. United States: N. p., 1991.
Web. doi:10.1142/S0217979292000463.
Balatsky, A. Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory. United States. https://doi.org/10.1142/S0217979292000463
Balatsky, A. 1991.
"Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory". United States. https://doi.org/10.1142/S0217979292000463. https://www.osti.gov/servlets/purl/5924084.
@article{osti_5924084,
title = {Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory},
author = {Balatsky, A},
abstractNote = {In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-{1/2} semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-{1/2} semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2){sub {kappa}=1} Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2){sub {kappa}=1} Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs.},
doi = {10.1142/S0217979292000463},
url = {https://www.osti.gov/biblio/5924084},
journal = {},
issn = {0217--9792},
number = 05n06,
volume = 06,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 1991},
month = {Tue Jan 01 00:00:00 EST 1991}
}