| The spectral correlations of the QCD Dirac operator can be computed in lattice QCD and described analytically by chiral random matrix theory and chiral perturbation theory. This very useful interplay of numerical and analytical methods allows for the extraction of low-energy constants, the analysis of finite-size effects, controlled extrapolations to the chiral limit, etc. However, at nonzero quark density the Dirac operator becomes non-hermitian, requiring more complicated analytical methods, e.g., non-hermitian random matrix theory. I will describe joint work with Jacques Bloch in which we have generalized the overlap lattice Dirac operator to nonzero density. This operator has exact zero modes at finite lattice spacing and therefore allows us to verify the RMT predictions for nontrivial topological charge. We have also generalized the domain-wall operator to nonzero density and shown that it converges to the overlap operator if the extent of the fifth dimension is taken to infinity. A few more applications will also be discussed. |
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