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Two-eigenfunction correlation in a multifractal metal and insulator | | E. Cuevas
; V. E. Kravtsov
; | | Date: |
2 Aug 2007 | | Abstract: | We consider the correlation of two single-particle probability densities
$|Psi_{E}({f r})|^{2}$ at coinciding points ${f r}$ as a function of the
energy separation $omega=|E-E’|$ for disordered tight-binding lattice models
(the Anderson models) and certain random matrix ensembles. We focus on the
models in the parameter range where they are close but not exactly at the
Anderson localization transition. We show that even far away from the critical
point the eigenfunction correlation show the remnant of multifractality which
is characteristic of the critical states. By a combination of the numerical
results on the Anderson model and analytical and numerical results for the
relevant random matrix theories we were able to identify the Gaussian random
matrix ensembles that describe the multifractal features in the metal and
insulator phases. In particular those random matrix ensembles describe new
phenomena of eigenfunction correlation we discovered from simulations on the
Anderson model. These are the eigenfunction mutual avoiding at large energy
separations and the logarithmic enhancement of eigenfunction correlations at
small energy separations in the two-dimensional (2D) and the three-dimensional
(3D) Anderson insulator. For both phenomena a simple and general physical
picture is suggested. | | Source: | arXiv, 0707.4585 | | Services: | Forum | Review | PDF | Favorites | |
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