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Quantum Hall system in Tao-Thouless limit
- Publication Year :
- 2007
-
Abstract
- We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the magnetic length). In the Tao-Thouless limit, $L_1\to 0$, the interacting many-electron problem is exactly diagonalized at any rational filling factor $\nu=p/q\le 1$. For odd $q$, the ground state has the same qualitative properties as a bulk ($L_1 \to \infty$) quantum Hall hierarchy state and the lowest energy quasiparticle exitations have the same fractional charges as in the bulk. These states are the $L_1 \to 0$ limits of the Laughlin/Jain wave functions for filling fractions where these exist. We argue that the exact solutions generically, for odd $q$, are continuously connected to the two-dimensional bulk quantum Hall hierarchy states, {\it ie} that there is no phase transition as $L_1 \to \infty$ for filling factors where such states can be observed. For even denominator fractions, a phase transition occurs as $L_1$ increases. For $\nu=1/2$ this leads to the system being mapped onto a Luttinger liquid of neutral particles at small but finite $L_1$, this then develops continuously into the composite fermion wave function that is believed to describe the bulk $\nu=1/2$ system. The analysis generalizes to non-abelian quantum Hall states.<br />Comment: 25 pages, 9 figures
- Subjects :
- Physics
Condensed matter physics
Condensed Matter - Mesoscale and Nanoscale Physics
FOS: Physical sciences
Landau quantization
Quantum Hall effect
Condensed Matter Physics
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
Electronic, Optical and Magnetic Materials
Particle in a one-dimensional lattice
Quantum spin Hall effect
Quantum mechanics
Composite fermion
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Spin Hall effect
Quantum spin liquid
Lattice model (physics)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....994d8f3893166e0e11d0c09981518708