Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

Abstract

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The <I>D</I>-theory then helps us to associate the continuum limit of the <i>(4+1)D </i>aniferromagnet to <i>4D </i>principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the<i> D</i>-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.