A constrained stochastic state selection method applied to quantum spin systems

TL;DR

This paper introduces a constrained stochastic state selection method to improve Monte Carlo simulations of large quantum spin systems, reducing statistical errors and enabling accurate energy estimations.

Contribution

The paper develops a constrained version of the stochastic state selection method, enhancing reliability and accuracy in quantum spin system simulations.

Findings

Reduced data errors in ground state energy estimation.

Successful evaluation of low-lying energy eigenvalues on larger lattices.

Support for the Neel ordered antiferromagnet theory.

Abstract

We describe a further development of the stochastic state selection method, which is a kind of Monte Carlo method we have proposed in order to numerically study large quantum spin systems. In the stochastic state selection method we make a sampling which is simultaneous for many states. This feature enables us to modify the method so that a number of given constraints are satisfied in each sampling. In this paper we discuss this modified stochastic state selection method that will be called the constrained stochastic state selection method in distinction from the previously proposed one (the conventional stochastic state selection method) in this paper. We argue that in virtue of the constrained sampling some quantities obtained in each sampling become more reliable, i.e. their statistical fluctuations are less than those from the conventional stochastic state selection method. In numerical calculations of the spin-1/2 quantum Heisenberg antiferromagnet on a 36-site triangular lattice we explicitly show that data errors in our estimation of the ground state energy are reduced. Then we successfully evaluate several low-lying energy eigenvalues of the model on a 48-site lattice. Our results support that this system can be described by the theory based on the spontaneous symmetry breaking in the semiclassical Neel ordered antiferromagnet.