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

C. M. Canali; V. E. Kravtsov

doi:10.1103/PhysRevE.51.R5185

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

Condensed Matter 2009-10-28 v1

Authors: C. M. Canali , V. E. Kravtsov

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

Keywords

random matrix ensembles U(N) invariance spontaneous symmetry breaking two-level correlation function level number variance

Cite

@article{arxiv.cond-mat/9504048,
  title  = {Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles},
  author = {C. M. Canali and V. E. Kravtsov},
  journal= {arXiv preprint arXiv:cond-mat/9504048},
  year   = {2009}
}

Comments

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

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

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