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') in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at s≈ -s'. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term var(n)=η 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, η playing the role of an order-parameter.
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