Lattice gauge theory with baryons at strong coupling
Abstract
We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4Nf) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(Nf) x U(Nf). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/Nc expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.
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