The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems

TL;DR

This paper introduces an enhanced stochastic state selection method combined with Lanczos algorithm to efficiently estimate ground state energies in large, frustrated quantum spin systems, demonstrating its effectiveness on a 48-site triangular lattice.

Contribution

The paper develops a novel combination of stochastic state selection with Lanczos approach for improved eigenvalue calculations in large quantum spin systems.

Findings

Estimated ground state energy: -0.1833 +/- 0.0003 per bond.

Method is efficient for large frustrated quantum systems.

Results are consistent with previous studies.

Abstract

We describe a further development of the stochastic state selection method, a new Monte Carlo method we have proposed recently to make numerical calculations in large quantum spin systems. Making recursive use of the stochastic state selection technique in the Lanczos approach, we estimate the ground state energy of the spin-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 our method is efficient in calculating energy eigenvalues of frustrated quantum spin systems on large lattices.