Multifractal dimensions for critical random matrix ensembles

Details Multifractal dimensions for critical random matrix ensembles Multifractal dimensions for critical random matrix ensembles

2012-01-30

arxiv.org/abs/1201.6353v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 9 figures

Scientific paper

Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q \le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $\chi$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1-\chi)[1+(q-1)\chi]^{-1}$, thus generalizing existing relations with relevance to the disorder driven Anderson--transition.

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