Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Off-diagonal long-range order in the fractional quantum Hall effect

Gun Sang Jeon, Michael Ronald Peterson, Jainendra K. Jain

Published Mar 24, 2005• 1 citation
OpenAlex

Related papers

Off-diagonal long range order in disordered quantum Hall systems

Shivaji L. Sondhi, Martin P. Gelfand

Physica B Condensed Matter•Aug 1, 1995•1 citation

Off-Diagonal Long-Range Order in Fractional Quantum-Hall-Effect States

Edward H. Rezayi, F. D. M. Haldane

We present evidence of off-diagonal long-range order in the incompressible fractional quantum Hall states at $\ensuremath{\nu}=\frac{1}{3} \mathrm{and} \frac{2}{5}$ Landau-level fillings. We construct correlation functions that exhibit this property only for incompressible quantum-Hall-effect states. In a compressible state no off-diagonal long-range order is observed.

Physical Review Letters•Oct 24, 1988•57 citations

Theory of the Fractional Quantum Hall Effect

Allan H. MacDonald

Recent Progress in Many-Body Theories•Jan 1, 1988•0 citations

Off-diagonal long-range order, oblique confinement, and the fractional quantum Hall effect

S. M. Girvin, Allan H. MacDonald

We demonstrate the existence of a novel type of off-diagonal long-range order in the fractional-quantum-Hall-effect (FQHE) ground state. This is revealed for the case of fractional filling factor \ensuremath{\nu}=1/m by application of Wilczek's ``anyon'' gauge transformation to attach m quantized flux tubes to each particle. The binding of the zeros of the wave function to the particles in the FQHE is a (2+1)-dimensional analog of oblique confinement in which a condensation occurs, not of ordinary particles, but rather of composite objects consisting of particles and gauge flux tubes.

Physical Review Letters•Mar 23, 1987•536 citations

Emergence and mechanism in the fractional quantum Hall effect

Jonathan Bain

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics•Nov 1, 2016•13 citations

Uncertainty principle and off-diagonal long-range order in the fractional quantum Hall effect

Лев П. Питаевский, S. Stringari

A natural generalization of the Heisenberg uncertainty principle inequality holding for non-Hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long-range order in the ground state of several one-dimensional (1D) systems with continuous-group symmetries. In this paper, we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long-range order in this two-dimensional (2D) problem is directly connected with the ${\mathit{q}}^{2}$ behavior of the static structure function S(q) at small momenta.

arXiv:cond-mat/9210023•Physical review. B, Condensed matter•Apr 15, 1993•14 citations
We demonstrate the existence of a novel type of off-diagonal long-range order in the fractional-quantum-Hall-effect (FQHE) ground state. This is revealed for the case of fractional filling factor \ensuremath{\nu}=1/m by application of Wilczek's ``anyon'' gauge transformation to attach m quantized flux tubes to each particle. The binding of the zeros of the wave function to the particles in the FQHE is a (2+1)-dimensional analog of oblique confinement in which a condensation occurs, not of ordinary particles, but rather of composite objects consisting of particles and gauge flux tubes.
A natural generalization of the Heisenberg uncertainty principle inequality holding for non-Hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long-range order in the ground state of several one-dimensional (1D) systems with continuous-group symmetries. In this paper, we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long-range order in this two-dimensional (2D) problem is directly connected with the q2{\mathit{q}}^{2}q2 behavior of the static structure function S(q) at small momenta.