The stochastic state selection method combined with the Lanczos approach to eigenvaluesin quantum spin systems

Abstract

We describe a further development of the stochastic state selection method, a new MonteCarlo method we have proposed recently to make numerical calculations in largequantum spin systems. Making recursive use of the stochastic state selectiontechnique in the Lanczos approach, we estimate the ground state energy of thespin-1/2 quantum Heisenberg antiferromagnet on a 48-site triangular lattice.Our result for the upper bound of the ground state energy is−0.1833 ± 0.0003 per bond. This value, being compatible with values from other work, indicates that ourmethod is efficient in calculating energy eigenvalues of frustrated quantum spin systems onlarge lattices.