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

TL;DR

This paper introduces a recursive stochastic state selection method for quantum spin systems that reduces sampling variance, demonstrated through numerical calculations on Heisenberg models showing improved accuracy in energy estimations.

Contribution

It extends existing stochastic methods with a recursive approach using intermediate states, significantly decreasing variance in Monte Carlo calculations for quantum spin systems.

Findings

Reduced variance in expectation value calculations

Accurate energy eigenvalues within 0.5% statistical error

Effective for large basis state systems (up to 3.6 x 10^7 states)

Abstract

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.