Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

Abstract

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.