F. Berruto

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

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 spectrum of this lattice gauge model: we identify the low-lying 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 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 〈ψψ〉 and isovector 〈ψσaψ〉 chiral condensates are zero to every order in the strong coupling expansion. In addition, we find that the chiral condensate 〈ψ(2)Lψ(1)Lψ(1)Rψ(2)R〉 is nonzero also on the lattice; this is the 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 spcetrum and we obtain an explicit construction of the lowest lying states for finite size Heisenberg antiferromagnetic chains.

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

We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which 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 li mit. 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 co ndensate 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 antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.

Spectrum of the two-flavor Schwinger model from the Heisenberg spin chain

We study the strong coupling limit of the 2-flavor lattice Schwinger model in the Hamiltonian formalism using staggered fermions. We show that the problem of finding the low-lying states is equivalent to solving the Heisenberg antiferromagnetic spin chain. We find good agreement with the continuum theory.

On the Correspondence Between Strongly Coupled QED 2 and QCD 2 with Antiferromagnetic Spin Chains

We analyse the correspondence between generalized Heisenberg chains and certain strongly coupled lattice gauge models. We construct the effective Hamiltonians of the strongly coupled lattice multiflavor Schwinger and ’t Hooft models and show their equivalence to a suitable SU(N) generalization of the quantum antiferromagnetic Heisenberg model.

On the doubling phenomenon in lattice Chern-Simons theories

Abstract We analyse the pure Chern-Simons theory on an Euclidean infinite lattice. We point out that, as a consequence of its symmetries, the Chern-Simons theory does not have an integrable kernel. Due to the linearity of the action in the derivatives, the situation is very similar to the one arising in the lattice formulation of fermionic theories. Doubling of bosonic degrees of freedom is removed by adding a Maxwell term with a mechanism similar to the one proposed by Wilson for the fermionic theories.

Lattice gauge theories and the Heisenberg antiferromagnetic chain

We study the strongly coupled2-flavor lattice Schwinger model and the SU (2)-color QCD2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin12 chain.

Chiral Symmetry Breaking in Strongly Coupled 1 + 1 Dimensional Lattice Gauge Theories

We analyse — within the hamiltonian formalism with staggered fermions — the patterns of chiral symmetry breaking for the strongly coupled Schwinger and U(.N c )-color ‘t Hooft models with one and two flavor of fermions. Using the correspondence between these strongly coupled gauge models and antiferromagnetic spin chains, we provide a rather intuitive picture of their ground states, elucidate their patterns of chiral symmetry breaking, and compute the pertinent chiral condensates. Our analysis evidences an intriguing relationship between the values of the lattice chiral condensates of the ‘t Hooft and Schwinger models with one flavor of fermions.