NONLINEAR FIELD ANALYSIS OF THE HUBBARD MODEL IN ONE AND TWO DIMENSIONS IN THE CONTINUUM LIMIT

Abstract

We investigate the Hubbard Hamiltonian's properties in the continuum limit by implementing the procedures of the Method of Coherent Structures (MCS). We obtain field equations of motion and analyse the phase dynamics of the resultant classical spin fields. We have performed analytical and numerical calculations to find appropriate physically acceptable solutions to the equations of motion in one-dimensional space. In two-dimensional space, among other types, we have found several different spin phases of vortex type, spiral patterns and parabolic spin arrangements. Our results are consistent with earlier Hartree–Fock finite-grid numerical simulations.