1994/01/03 by M. Kasner, Kasner, M.
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Magnetic properties of thin films #Quantum and electron transport phenomena #Surface and Thin Film Phenomena #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9401002
10 pages, LATEX-file
arxiv created 1994/01/03 · openalex publication_date 1994/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the hierarchical theory of the fractional quantum Hall effect, the low--energy behaviour of a daughter state in the next level of the hierarchy is described by an interacting system of quasiparticles of the parent state. Taking the filled lowest Landau level as the parent state, we examine analytically the quantitative consequences of this approach for electrons interacting via a pseudopotential interaction. It is shown that the ground state energy per particle in the daughter state at a filling factor 2/3 is exactly equal to that of a system of quasiholes in the parent state with half filling, precisely as predicted by the hierarchical approach. This is achieved with \em only up to two--particle interactions in the effective Hamiltonian for the quasiholes. Their single particle energy and two--particle interaction are derived. The results are generalized to the other filling factors attainable from the filled Landau level.