| The theoretical description of strongly correlated systems is a principle area of work in theoretical condensed matter physics because of the limitations of perturbation methods. In this thesis I discuss two important such systems by direct (although approximate) calculations.; Chapter I is mainly the composition of two publications in which we have discussed the molecular polaron with q{dollar}sp2{dollar} coupling. In Sections 2, 3 and 4, we use a solvable mean field version of the q{dollar}sp2{dollar} polaron to test a new non-perturbative functional integral formalism using holomorphic fermion and boson variables.{dollar}sp1{dollar} Section 5 is a derivative of the above mean field calculation.{dollar}sp2{dollar} It presents a mathematical theorem for the calculation of a class of averages arising in the mean field calculation.; In Chapter II and III we discuss the Heisenberg antiferromagnetic Hamiltonian with spin 1/2 which is the form taken by the Hamiltonian of a resonating valence bond (RVB) system where the intra-atomic repulsion is large. In Chapter II we use a trial wave function to calculate the ground state energy{dollar}sp3{dollar} and excitation spectrum.{dollar}sp4{dollar} In Chapter III, we discussed a mean field theory of the resonating valence bond state and try to explore the correlation function behavior in a 1D chain with arbitrary spin, integral or half integral. ftn{dollar}sp1{dollar}Y. Fan and B. Goodman, Phys. Rev. 35, 7694 (1987). {dollar}sp2{dollar}Y. Fan and B. Goodman, J. Phys. A 20, 143 (1987). {dollar}sp3{dollar}Y. Fan and M. Ma, Phys. Rev. 37, 1820 (1988). {dollar}sp4{dollar}Y. Fan and M. Ma, Bull. Amer. Phys. Soc. 33, 627 (1988). |
