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Replica treatment of non-Hermitian disordered Hamiltonians

Shinsuke M. Nishigaki·Alex Kamenev
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Abstract

We employ the fermionic and bosonic replicated nonlinear sigma models to treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian random matrix Hamiltonians. Using saddle point approach combined with Borel resummation procedure we derive the exact large-N results for microscopic density of states in all three ensembles. We also obtain tails of the density of states as well the two-point function for the unitary ensemble.

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Shinsuke M. Nishigaki, Alex Kamenev. 2001-09-13. Replica treatment of non-Hermitian disordered Hamiltonians. https://doi.org/10.1088/0305-4470%2F35%2F21%2F307

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