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It is shown that the parametric spectral statistics in the critical randommatrix ensemble with multifractal eigenvector statistics are identical to thestatistics of correlated 1D fermions at finite temperatures. For weakmultifractality the effective temperature of fictitious 1D fermions isproportional to (1-d_{n})/n, where d_{n} is the fractal dimension found fromthe n-th moment of inverse participation ratio. For large energy and parameterseparations the fictitious fermions are described by the Luttinger liquid modelwhich follows from the Calogero-Sutherland model. The low-temperatureasymptotic form of the two-point equal-parameter spectral correlation functionis found for all energy separations and its relevance for the low temperatureequal-time density correlations in the Calogero-Sutherland model isconjectured.Comment: 4 pages, Revtex, final journal versio

Energy level dynamics in systems with weakly multifractal eigenstates: Equivalence to one-dimensional correlated fermions at low temperatures