Pseudo-Hermitian β-Laguerre Ensemble with Unbound Metric

The consequences an unbound metric has in the pseudo-Hermitian β-Laguerre ensemble are investigated. By constructing a family of pseudo-Hermitian matrices iso-spectral to the matrices of the Hermitian β-Laguerre ensemble, it is shown that under arbitrarily small perturbations the matrices undergo a spontaneous symmetry break in which pairs of conjugate eigenvalues move into the complex plane. The delocalization of the eigenvectors of the complex eigenvalues is studied. A tight-bind model is constructed with the matrices of the family.