Static spin susceptibility in the \(t\)-\(J\) model (Q2461115)

The paper is devoted to the presentation of numerical results for the static spin susceptibility in the \(t\)-\(J\) model on the base of analytic expressions obtained that are applicable in the entire temperature range and for any concentration of doped holes. First, the authors consider the \(t\)-\(J\) model in terms of the Hubbard operators in 2-D square lattice. The hopping integrals and the exchange interaction are taken into account only for the nearest neighboring sites of the lattice. Due to, the parameters \(t\) and \(J\) independent parameters of the model are considered. Then, the static spin susceptibility in the \(t\)-\(J\) model is written by using thermodynamic Green's function of Fourier components of the spin operator and Kubo-Mori scalar product. This susceptibility is evaluated by using the equations of motion for spin operators expressed in terms of Hubbard operators, but its approximate expression is obtained in a framework of the relaxation function formalism. First, the representation for a force operator is obtained, and the correlation functions are introduced. To calculate the correlation function the authors use the decoupling technique which is equivalent to the approximation of coupled modes for the one-time correlation function. In the mean-field approximation, the mixed contribution to the correlation function can be omitted. The evaluation of the multisite correlation functions in the mean-field approximation introduces the factors that take the approximate nature of the decoupling into account by renormalizing the corresponding vertex, namely: (i) accounting for the spin-hole coupling; (ii) and (iii) accounting for the vertex for spin correlation functions of the respective nearest neighbors and next-to-nearest neighbors. These three factors are determined when computing self-consistently the static susceptibility numerically. In calculation these parameters, the sum rule is used as one of the additional equations. The other two equations are chosen by considering four cases: (i) zero temperature, no doping, and nonvanishing magnetization; (ii) zero temperature, low doping, and nonvanishing magnetization; (iii) zero temperature, overcritical doping, and vanishing magnetization; (iv) finite temperature. The numerical results obtained for these four cases are compared with the results of other authors, showing a qualitative agreement with the experiment.