Abstract
We develop a supersymmetric virial expansion for two-point correlation functions of almost diagonal Gaussian random matrix ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple applications in physics and can be used to study the universal properties of time-reversal invariant disordered systems which are either insulators or close to the Anderson localization transition. We derive a two-level contribution to the correlation functions of the generic ADRMT and apply these results to the critical (multifractal) power law banded ADRMT. Analytical results are compared with numerical ones.
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