Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles
arXiv:cond-mat/9504048 · doi:10.1103/PhysRevE.51.R5185
Abstract
It is shown that the two-level correlation function $R(s,s')$ in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term ${\rm var}(n)=ηn$ that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, $η$ playing the role of an order-parameter.
13 pages, REVTEX 3.0, 1 figure not included (postscript file available on request)