Preserving topology while breaking chirality: From chiral orthogonal to anti-symmetric Hermitian ensemble

Abstract

We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian orthogonal ensemble (Cartan class B|DI) and the ensemble of antisymmetric Hermitian random matrices (Cartan class B|D). It enjoys the special feature that, depending on the matrix dimension N, it has exactly ν = 0 (1) zero-mode for N even (odd), throughout the symmetry transition. This topological protection is reminiscent of properties of topological insulators. We show that our ensemble represents a Pfafian point process which is typical for such transition ensembles. On a technical level, our results follow from th..