Nonuniversal Behavior of thek-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the k-body embedded unitary ensemble in the limit of a large matrix dimension. We identify the transition point between a semicircle and a Gaussian shape. The transition also affects the spectral fluctuations which deviate from the Wigner-Dyson form and become Poissonian in the limit k<<m<<l. Here m is the number of fermions and l the number of degenerate single-particle states.