Coupled Cluster Approximation to the \emph{t-J} Model

We study the ground state of the one-dimensional \emph{t-J} model with a single hole using the well known Coupled Cluster Method (CCM). The Hamiltonian includes a kinetic energy term \emph{t} which represents electron hopping from atomic site to atomic site with a probability which is proportional to the overlap of their (localized) wave functions. There is also an intra-atomic Coulomb energy $\emph{U}$ taken to be large so that the region of parameter space of interest is $t/U\ll1$. The CCM is a well-known scheme for evaluating many-particle systems wherein an operator $S$ is introduced as $\left\vert \Psi\right\rangle =e^{s}\left\vert \Psi_{0}\right\rangle $ and represents the many-particle excitations of the system. A set of non-linear equations are then generated from $\left\langle \Psi_{0}\right\vert H\left\vert \Psi _{n}\right\rangle =0$ and $\left\langle \Psi_{0}\right\vert H\left\vert \Psi_{0}\right\rangle =E_{0}$ in which the ground state energy may then be calculated.