Order from disorder in lattice QCD at high density

Abstract

We investigate the properties of the ground state of strong coupling lattice QCD at finite density. Our starting point is the effective Hamiltonian for color singlet objects, which looks at lowest order as an antiferromagnet, and describes meson physics with a fixed baryon number background. We concentrate on uniform baryon number backgrounds (with the same baryon number on all sites), for which the ground state was extracted in an earlier work, and calculate the dispersion relations of the excitations. Two types of Goldstone boson emerge. The first, antiferromagnetic spin waves, obey a linear dispersion relation. The others, ferromagnetic magnons, have energies that are quadratic in their momentum. These energies emerge only when fluctuations around the large-N_c ground state are taken into account, along the lines of ``order from disorder'' in frustrated magnetic systems. Unlike other spectrum calculations in order from disorder, we employ the Euclidean path integral. For comparison, we also present a Hamiltonian calculation using a generalized Holstein-Primakoff transformation. The latter can only be constructed for a subset of the cases we consider.