On the correspondence between the strongly coupled 2-flavor lattice Schwinger model and the Heisenberg antiferromagnetic chain

We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered Fermions and the Hamiltonian approach to latt ice gauge theories. Using the correspondence between the low-lying states o f the 2-flavor strongly coupled lattice Schwinger model and the antiferroma gnetic Heisenberg chain established in a previous paper, we explicitly comp ute the mass spectrum of this lattice gauge model: we identify the low-lyin g excitations of the Schwinger model with those of the Heisenberg model and compute the mass gaps of other excitations in terms of vacuum expectation values (v.e.v.'s) of powers of the Heisenberg Hamiltonian and spin-spin cor relation functions. We find a satisfactory agreement with the results of th e continuum theory already at the second order in the strong coupling expan sion. We show that the pattern of symmetry breaking of the continuum theory is well reproduced by the lattice theory; we see indeed that in the lattic e theory the isoscalar [<(psi)over bar>psi] and isovector [<(psi)over bar>s igma(a)psi] chiral condensates are zero to every order in the strong coupli ng expansion. In addition, we find that the chiral condensate [<(psi)over b ar>((2))(L)<(psi)over bar>((1))(L)<(psi)over bar>((1))(R)<(psi)over bar>((2 ))(R)] is nonzero also on the lattice; this is the relic in this lattice mo del of the axial anomaly in the continuum theory. We compute the v.e.v.'s o f the spin-spin correlators of the Heisenberg model which are pertinent to the calculation of the mass spcetrum and we obtain an explicit construction of the lowest lying states for finite size Heisenberg antiferromagnetic ch ains. (C) 1999 Academic Press.