The Stochastic State Selection Method for Energy Eigenvalues in the Shastry-Sutherland Model

TL;DR

This paper introduces a stochastic method to efficiently estimate energy eigenvalues in the Shastry-Sutherland model, demonstrating its effectiveness on small and large lattices and providing insights into phase transitions.

Contribution

The paper applies a novel stochastic state selection method to the Shastry-Sutherland model, enabling accurate energy evaluations with limited states and analyzing phase transitions.

Findings

Method accurately estimates energy eigenvalues in frustrated systems.

Restructured state representations improve evaluation accuracy.

Results support the existence of an intermediate spin-gap phase.

Abstract

We apply a recently developed stochastic method to the Shastry-Sutherland model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State Selection Method here, enables us to evaluate expectation values of powers of the Hamiltonian with very limited number of states. In this paper we first apply it to the 4x4 Shastry-Sutherland system, where one can easily obtain the exact ground state, in order to demonstrate that the method works well for this frustrated system. We numerically show that errors of the evaluations depend much on representations of the states and that the restructured representation is better than the normal one for this model. Then we study the 8x8 system to estimate energy eigenvalues of the lowest S=1 state as well as of the lowest excited S=0 state, where S denotes the total spin of the system. The results, which are in good accordance with our previous data obtained by the Operator Variational method, support that an intermediate spin-gap phase exists between the singlet dimer phase and the magnetically ordered phase. Estimates of the critical coupling and of the spin gap for the transition from the dimer phase to the intermediate phase are also presented.