Towards extremely dense matter on the lattice

Abstract

Quantum chromodynamics (QCD) is expected to have a rich phase structure. It is empirically known to be difficult to access low-temperature and nonzero chemical potential μ regions in lattice QCD simulations. We address this issue in lattice QCD with the use of a dimensional reduction formula for the fermion determinant. We investigate the spectral properties of a reduced matrix of the reduction formula. Lattice simulations with different lattice sizes show that the eigenvalues of the reduced matrix follow a scaling law for the temporal size Nt. The properties of the fermion determinant are examined using the reduction formula. We find that, as a consequence of the Nt-scaling law, the fermion determinant becomes insensitive to μ as T decreases, and is μ-independent at T = 0 forμ