Chiral symmetry breaking on the lattice: A study of the strongly coupled lattice Schwinger model

We reexamine the strong-coupling limit of the Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they possess a discrete axial invariance that forbids a fermion mass and must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory, We show that this discrete symmetry is indeed broken spontaneously in the strong-coupling limit. Expanding around a gauge-invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong-coupling expansion and compute the masses of the low-lying bosonic excitations as well as the chiral condensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong-coupling perturbation theory. We also find the exact ground state of the antiferromagnetic Ising spin chain with the long-range Coulomb interaction, which determines the nature of the ground state in the strong-coupling limit.