Preserving topology while breaking chirality: from chiral orthogonal to anti-symmetric Hermitian ensemble (original) (raw)
2019, Journal of Statistical Mechanics: Theory and Experiment
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 Pfaffian point process which is typical for such transition ensembles. On a technical level, our results follow from the applicability of the Harish-Chandra integral over the orthogonal group. The matrixvalued kernel determining all eigenvalue correlation functions is explicitly constructed in terms of skeworthogonal polynomials, depending on the topological index ν = 0, 1. These polynomials interpolate between Laguerre and even (odd) Hermite polynomials for ν = 0 (1), in terms of which the two limiting symmetry classes can be solved. Numerical simulations illustrate our analytical results for the spectral density and an expansion for the distribution of the smallest eigenvalue at finite N .
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.