Effect of vacancies in spin models

Abstract

The study of t-J like models has always been of interest since it is believed to describe high critical temperature (T C ) superconductivity in cuprates(CuO 2 ). In this thesis we try to understand t-J like models by exploring the phase diagrams of the such toy models. The first chapter of thesis describes the constituents of t-J models which are Heisenberg and Hubbard model(in half-filling limit). Both the models are studied using Exact Diago- nalization. The correspondence of both the models are shown by plotting 2 point spatial spin correlation. In the second chapter we study the J 1 − J 2 Anti-ferromagnetic Heisenberg system, a highly frustated model which exhibits phase diagram. We study this system by using Semi- classical Monte Carlo with semi-classical dimers as proxy for quantum fluctuations. In the last part we see the changes in phase diagram on introducing vacancies/holes in the model to simulate an effective t-J like model.