Lattice gauge theory with baryons at strong coupling

TL;DR

This paper investigates the effective Hamiltonian of strong-coupling lattice QCD with non-zero baryon density, revealing symmetry breaking patterns and phase behavior through a sigma model analysis.

Contribution

It introduces a generalized antiferromagnetic Hamiltonian for lattice QCD at strong coupling, incorporating baryon density effects and analyzing symmetry breaking using a sigma model approach.

Findings

Spontaneous chiral symmetry breaking in vacuum for nearest and nnn theories.

Symmetry breaking patterns depend on baryon density.

Effective Hamiltonian includes next-nearest-neighbor terms that alter symmetry.

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(4N_f) 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(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c 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.