Vacuum structure and chiral-symmetry breaking in (2+1)-dimensional lattice gauge theories with fermions.

Abstract

We study further the vacuum structure and chiral-symmetry breaking in Hamiltonian lattice gauge theory with fermions. Attention is paid to (2+1)-dimensional systems. For the fermion sector, a unitary transformation and the variational method are employed. The antiferromagnetic nature of the unitarily transformed Hamiltonian and mesons as spin waves are presented at strong coupling, and the relevance for high-${T}_{c}$ superconductivity is discussed. The vacuum state of the full theory is assumed to be the combination of the variational fermion vacuum state and the exact ground state of the modified Hamiltonian for pure gauge theory of Guo and co-workers. The existing problems in the modified theory are pointed out as well. The chiral condensates in ${\mathrm{QED}}_{3}$ and ${\mathrm{QCD}}_{3}$ are calculated and the scaling behavior is observed in the crossover regime.