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In this paper we propose the recursive stochastic state selection method, anextension of the recently developed stochastic state selection method in MonteCarlo calculations for quantum spin systems. In this recursive method we useintermediate states to define probability functions for stochastic stateselections. Then we can diminish variances of samplings when we calculateexpectation values of the powers of the Hamiltonian. In order to show theimprovement we perform numerical calculations of the spin-1/2anti-ferromagnetic Heisenberg model on the triangular lattice. Examiningresults on the ground state of the 21-site system we confide this method in itseffectiveness. We also calculate the lowest and the excited energy eigenvaluesas well as the static structure factor for the 36-site system. The maximumnumber of basis states kept in a computer memory for this system is about 3.6 x10**7. Employing a translationally invariant initial trial state, we evaluatethe lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems