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

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

1995-04-12

arxiv.org/abs/cond-mat/9504048v1

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevE.51.R5185

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 ${\rm var}(n)=\eta n$ 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.

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