Perturbational Method for the Numerical Evaluation of the Ground-State Energy of the Heisenberg Model

A perturbational method is developed and applied to the numerical calculation for the energy of the ground state E_g of antiferromagnetic Heisenberg model of finite size systems. In this method the system is divided into two subsystems and each one is treated exactly, while the interactions between the subsystems are taken into account by the second order perturbation. This process saves the memory space of computer, and moreover the relative error is very small and decreases as the size of system is increased. Actual calculations for the triangular lattice are performed up to the number of spins N=36 and E_g for the infinite lattice is estimated as - (1.04±0.01)N|J|, where |J| is the exchange integral.