Theoretical Studies of Strongly Correlated Systems.

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 ^2 coupling. In Sections 2, 3 and 4, we use a solvable mean field version of the q ^2 polaron to test a new non-perturbative functional integral formalism using holomorphic fermion and boson variables.^1 Section 5 is a derivative of the above mean field calculation. ^2 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^3 and excitation spectrum.^4 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 ^1Y. Fan and B. Goodman, Phys. Rev. 35, 7694 (1987). ^2Y. Fan and B. Goodman, J. Phys. A 20, 143 (1987). ^3Y. Fan and M. Ma, Phys. Rev. 37, 1820 (1988). ^4 Y. Fan and M. Ma, Bull. Amer. Phys. Soc. 33, 627 (1988).