On the Correspondence Between the Strongly Coupled 2-Flavor Lattice Schwinger Model and the Heisenberg Antiferromagnetic Chain

TL;DR

This paper explores the strong coupling limit of the 2-flavor lattice Schwinger model, establishing a correspondence with the Heisenberg antiferromagnetic chain, and computes mass gaps and condensates showing agreement with continuum theory.

Contribution

It explicitly relates the lattice Schwinger model to the Heisenberg chain, computing mass gaps and condensates, and reproduces symmetry breaking patterns of the continuum theory.

Findings

Mass gaps agree with continuum results at second order in strong coupling.

Lattice theory reproduces symmetry breaking patterns of the continuum.

Chiral condensate persists on the lattice, indicating axial anomaly relic.

Abstract

We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Using the correspondence between the low-lying states of the 2-flavor strongly coupled lattice Schwinger model and the antiferromagnetic Heisenberg chain established in a previous paper, we explicitly compute the mass gaps of the other excitations in terms of vacuum expectation values (v.e.v.'s) of powers of the Heisenberg Hamiltonian and spin-spin correlation functions. We find a satisfactory agreement with the results of the continuum theory already at the second order in the strong coupling expansion. 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 lattice theory the isoscalar and isovector chiral condensates are zero to every order in the strong coupling expansion. In addition, we find that the chiral condensate $<\bar{\psi}_{L}^{(2)}\bar{\psi}_{L}^{(1)}\psi_{R}^{(1)}\psi_{R}^{(2)}>$ is non zero also on the lattice; this is the only relic in this lattice model of the axial anomaly in the continuum theory. We compute the v.e.v.'s of the spin-spin correlators of the Heisenberg model which are pertinent to the calculation of the mass spectrum and obtain an explicit construction of the lowest lying states for finite size Heisenberg Hamiltonian chains.