Coupling of holes in the t-J model on an infinite plane

Abstract

In a wide range of parameters the low-energy dynamics of the extended Hubbard model can be described by the effective hamiltonian of the t-J type. The hamiltonian contains terms of the static interaction between holes. For a certain parameter range this interaction corresponds to an attraction. Parameters presumbly realized in La 2CuO 4 fall into this range and for them the effective hamiltonian is reduced to the standard t-J hamiltonian. The static attraction assisted by processes of a spin-bond softening in the vicinity of holes is shown to play a crucial role in the binding of holes. The energy band scheme, symmetry and binding energy of two-hole states are considered for the effective hamiltonian and its Ising analogue on an infinite plane. The spin-wave approximation is used in the calculations. For the hamiltonian the lowest energy is achieved in a d-type state with zero wave vector, while in its Ising analogue a crossover between this state and the p-type state in the point (π/ a, 0) of the Brillouin zone occurs at moderate values of parameters. In the case of the standard t-J hamiltonian the absolute value of the binding energy obtained on an infinite plane is markedly smaller than that on small lattices where the influence of finite-size effects is essential.