Quantum Hall system in Tao-Thouless limit
2008 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 77, no 15, 155308- p.Article in journal (Refereed) Published
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 2π/L1, where L1 is a circumference of the torus (in units of the magnetic length). In the Tao-Thouless limit L1→0, the interacting many-electron problem is exactly diagonalized at any rational filling factor ν=p/q≤1. For odd q, the ground state has the same qualitative properties as a bulk (L1→∞) quantum Hall hierarchy state and the lowest-energy quasiparticle excitations have the same fractional charges as in the bulk. These states are the L1→0 limits of the Laughlin and 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—i.e., that there is no phase transition as L1→∞ for filling factors where such states can be observed. For even-denominator fractions, a phase transition occurs as L1 increases. For ν=1/2 this leads to the system being mapped onto a Luttinger liquid of neutral particles at small but finite L1; this then develops continuously into the composite fermion wave function that is believed to describe the bulk ν=1/2 system. The analysis generalizes to non-Abelian quantum Hall states.
Place, publisher, year, edition, pages
2008. Vol. 77, no 15, 155308- p.
IdentifiersURN: urn:nbn:se:su:diva-24941DOI: 10.1103/PhysRevB.77.155308ISI: 000255457400078OAI: oai:DiVA.org:su-24941DiVA: diva2:198559