Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-03-22
Nucl.Phys. B700 (2004) 361
Physics
Condensed Matter
Disordered Systems and Neural Networks
17 pages, 4 figures; discussions on superconductivity removed
Scientific paper
10.1016/j.nuclphysb.2004.08.035
We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law ${{\cal H}_{ij}}\sim |i-j|^{-\alpha}$. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states and the two-level correlation function by mapping the chRBM onto a nonlinear sigma model. We also put forward, by exploiting the relation between the chRBM at $\alpha=1$ and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to QCD.
Garcia-Garcia Antonio M.
Takahashi Kazutaka
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