Analytic operator approach to fermionic lattice field theories

Abstract

An analytic Lanczos algorithm previously used to extract the spectrum of bosonic lattice field theories in the continuum region is extended to theories with fermions. The method is illustrated in detail for the (1 + 1)-dimensional Gross-Neveu model. All parameters in the model (coupling, lattice size N, number of fermion flavors NF, etc.) appear explicitly in analytic formulas for matrix elements of the hamiltonian. The method is applied to the calculation of the collective field vacuum expectation value and the mass gap, and excellent agreement obtained with explicit results available from the large NF solution of the model.