arXiv:cond-mat/9409012 · Physical Review Letters

Compressible ν=1/2 state in a finite size study?

Jainendra K. Jain

Published Aug 15, 1994• 7 citations

Abstract

For a meaningful numerical investigation of thermodynamic properties, systems bigger than the correlation length need to be studied. Fortunately, due to the existence of a gap, the incompressible fractional quantum Hall states have a finite correlation length, which, for some states (e.g., 1/3, 2/5) happens to be smaller than the system sizes that can be studied. On the other hand, since the Fermi liquid is a critical state with power law correlations, one might expect that finite system studies are less likely to provide any conclusive results. Rezayi and Read (RR) [1] have recently claimed that their numerical study provides “convincing evidence for the correctness of the Halperin-Lee-Read [2] theory of a compressible fermi-liquid-like state ” at ν = 1/2. We argue below that their study sheds little light on the on the thermodynamic nature of the compressible state at ν = 1/2. RR have studied N-electron systems at flux Nφ = 2(N − 1) in the spherical geometry. Their numerical calculations test a special case of the composite fermion theory [3], which provides a general relationship between the low-energy spectra and eigenstates of the systems at Nφ and N ∗ φ = Nφ − 2(N − 1). Extensive calculations of this type have been performed in the past, including for Nφ = 2(N −1) [4–6]. RR merely interpret the results differently. For

DOI: 10.1103/physrevlett.73.1051

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