5. Theoretical Physics (CSN4)

QCD at Finite Density and the Sign Problem

by Prof. Jacobus Verbaarschot (Stony Brook University)

Auletta A1 (LNF)

Auletta A1


Via Enrico Fermi, 40 00044 Frascati (Roma)
Because of the phase of the fermion determinant lattice QCD at nonzero chemical potential cannot be simulated by standard stochastic algorithms. However, if the sign problem is not severe, various independent methods give consistent results. We will investigate the severity of the sign problem by means of chiral perturbation theory. The distribution of the average phase factor, the chiral condensate and the baryon number will be derived and the overlap problem will be discussed. We compare various observables evaluated in QCD and in phase quenched QCD and give quantitative estimates for the contribution due to the phase of the fermion determinant. We will ask the question if there is a preferred class of observables with weak correlations with the phase factor which can be evaluated despite a severe sign problem. The relation between the Dirac spectrum and the sign problem will be discussed. We will illustrate these questions by explicit calculations in one dimensional lattice QCD and random matrix theory. Finally, implications for other nonhermitean Dirac operators suchas the Wilson Dirac operator at nonzero lattice spacing will be discussed.