Complex spectrum of QCD at finite density
We consider the spectrum of transfer matrix eigenvalues associated with Polyakov loops in lattice QCD at strong coupling. The transfer matrix at finite density is non-Hermitian, and its eigenvalues become complex as a manifestation of the sign problem. We show that the global symmetries of finite-density QCD ensure that the complex eigenvalues are part of a complex conjugate pair, and they lead to sinusoidally modulated decay in Polyakov loop correlation functions. We argue that the results reflect oscillatory behavior in color-charge densities reminiscent of density-density correlation functions in liquids, and it is generic in spin models for QCD at finite density, as well as phenomenological models using complex saddle points.