Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles

Abstract

It is shown that the two-level correlation function $R(s,s^{\prime })$ in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at $s\approx -s^{\prime }$. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term $\mathrm{var}(n)=\eta n$ 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, $\eta$ playing the role of an order-parameter.

13 pages, REVTEX 3.0, 1 figure not included (postscript file available on request)

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