Local properties of the t-J model in a two-pole approximation within COM

In this work, we study the t-J model using a two-pole approximation within the composite operator method. We choose a basis of two composite operators – the constrained electrons and their spin-fluctuation dressing – and approximate their currents in order to compute the corresponding Green's functions. We exploit the algebraic constraints obeyed by the basis operators to close a set of self-consistent equations that is numerically solved. This allows to determine the physical parameters of the system such as the spin–spin correlation function and the kinetic energy. Our results are compared to those of an exact numerical method on a finite system to assess their reliability. Indeed, a very good agreement is achieved through a far less numerically demanding and a more versatile procedure. We show that by increasing the hole doping, anti-ferromagnetic correlations are replaced by ferromagnetic ones. The behavior on changing temperature and exchange integral is also studied and reported.