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Overlap Dirac operator at nonzero chemical potential and random matrix theory

Bloch, Jacques and Wettig, Tilo (2006) Overlap Dirac operator at nonzero chemical potential and random matrix theory. Physical Review Letters 97, 012003.

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Other URL: http://link.aps.org/abstract/PRL/V97/E012003

Abstract

We $^{ }$ show how to introduce a quark chemical potential in the $^{ }$ overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation $^{ }$ and has exact zero modes. It is no longer $\gamma$$_{5}$$^{ }$ Hermitian, but its nonreal eigenvalues still occur in pairs. We $^{ }$ compute the spectral density of the operator on the lattice $^{ }$ and show that, for small eigenvalues, the data agree with $^{ }$ analytical predictions of non-Hermitian chiral random matrix theory for both $^{ }$ trivial and nontrivial topology. We also explain an observed change $^{ }$ in the number of zero modes as a function of $^{ }$ chemical potential.