Abstract
We consider the block band matrices, i.e. the Hermitian matrices HN,N={pipe}Λ{pipe}W with elements Hjk,αβ where j,k ∈ Λ =[1,m]d ∩ ℤd (they parameterize the lattice sites) and α β = 1,...., W(they parameterize the orbitals on each site). The entries Hjk,α β are random Gaussian variables with mean zero such that 〈 Hj1k1,α1β1,Hj2k2,α2β2〉 =δj1k2δj2k1δα1β2δβ1α2Jj1k1 where J=1/W+α Δ /W, α < 1/4d. This matrices are the special case of Wegner's W-orbital models. Assuming that the number of sites {pipe}Λ{pipe} is finite, we prove universality of the local eigenvalue statistics of HN for the energies {pipe}λ0{pipe}< √2.
Original language | English (US) |
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Pages (from-to) | 466-499 |
Number of pages | 34 |
Journal | Journal of Statistical Physics |
Volume | 155 |
Issue number | 3 |
DOIs | |
State | Published - May 2014 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Keywords
- Band matrices
- Random matrices
- Universality
- Wegner model