Random Matrix Models for Dirac Operators at finite Lattice Spacing

Details Random Matrix Models for Dirac Operators at finite Lattice Spacing Random Matrix Models for Dirac Operators at finite Lattice Spacing

2011-10-12

arxiv.org/abs/1110.2690v2

PoS LATTICE 2011, 312 (2011)

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 6 figures, Proceedings for the XXIX International Symposium on Lattice Field Theory, July 10 -- 16 2011, Squaw Valley

Scientific paper

We study discretization effects of the Wilson and staggered Dirac operator with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a determinantal expression over complex pairs of eigenvalues, and real eigenvalues corresponding to eigenvectors of positive or negative chirality as well as for the eigenvalue densities. The explicit dependence on the lattice spacing can be readily read off from our results which are compared to numerical simulations of Wilson-chRMT. For the staggered Dirac operator we have studied random matrices modeling the transition from non-degenerate eigenvalues at non-zero lattice spacing to degenerate ones in the continuum limit.

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