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

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.

17 pages, 4 figures

References in corpus (13)

• Correlated Electrons in High Temperature Superconductors
• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Quantum Phase Transitions in the Shastry-Sutherland Model for $\mathbf{SrC}{\mathbf{u}}_2(\mathbf{B}{\mathbf{O}}_3{)}_2$
• Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model
• Phase Diagram of the quadrumerized Shastry-Sutherland Model
• Quantum Phases of the Shastry-Sutherland Antiferromagnet
• First order transition between magnetic order and valence-bond order in a 2D frustrated Heisenberg model
• Path-Integral Renormalization Group Method for Numerical Study of Strongly Correlated Electron Systems
• Two-Triplet-Dimer Excitation Spectra in the Shastry-Sutherland Model for SrCu_2(BO_3)_2
• An Improvement on the Negative Sign Problem in Numerical Calculations of a Quantum Spin System
• A New Approach to Stochastic State selections in Quantum Spin Systems
• Numerical Study of Excited States in the Shastry-Sutherland Model

Cited by in corpus (5)

• Far-infrared spectroscopy of spin excitations and Dzyaloshinskii-Moriya interactions in a Shastry-Sutherland compound SrCu${}_2$(BO${}_3$)$_2
• A Recursive Method of the Stochastic State Selection for Quantum Spin Systems
• An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method
• The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems
• A constrained stochastic state selection method applied to quantum spin systems