Ground-state degeneracy and fractionally charged excitations in the anomalous quantum Hall effect
1984; American Physical Society; Volume: 30; Issue: 2 Linguagem: Inglês
10.1103/physrevb.30.1069
ISSN1095-3795
Autores Tópico(s)Quantum Information and Cryptography
ResumoThe Hamiltonian describing two-dimensional electrons in a high magnetic field is diagonalized exactly for a small number of particles. In addition to the energy spectrum the mean occupation number $\ensuremath{\rho}(j)=〈{C}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{C}_{j}〉$ of the $j$th Landau state in the lowest Landau level is also calculated. For $\ensuremath{\nu}=\frac{n}{m}$ with $m$ an odd integer, $\ensuremath{\rho}(j)$ has a period $m [\ensuremath{\rho}(j)=\ensuremath{\rho}(j+m)]$, and there are $m$ distinct ground states---in striking analogy with a one-dimensional charge-density-wave system. In terms of $\ensuremath{\rho}(j)$, profiles of the ⅓ kinks are obtained in the ground state for $\ensuremath{\nu}$ close to ⅓. Creation energy of the kink is obtained from the energy gap. The $\ensuremath{\nu}=\frac{1}{2}$ case is markedly different.
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