Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2000-02-08
Phys. Rev. B, 62 (2000) 9888
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, Revtex, final journal version
Scientific paper
10.1103/PhysRevB.62.9888
It is shown that the parametric spectral statistics in the critical random matrix ensemble with multifractal eigenvector statistics are identical to the statistics of correlated 1D fermions at finite temperatures. For weak multifractality the effective temperature of fictitious 1D fermions is proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from the n-th moment of inverse participation ratio. For large energy and parameter separations the fictitious fermions are described by the Luttinger liquid model which follows from the Calogero-Sutherland model. The low-temperature asymptotic form of the two-point equal-parameter spectral correlation function is found for all energy separations and its relevance for the low temperature equal-time density correlations in the Calogero-Sutherland model is conjectured.
Kravtsov Vladimir E.
Tsvelik Alexei M.
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