Numerical methods for spin models

Cui Xiao-Bo, Zhide Chen

We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about 10 − n times of the exact numerical result for the n th excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.

M. S. Makivić

S. Ramasesha

David S. Kung, R. Blankenbecler, Robert L. Sugar

The general application of the projector Monte Carlo method to spin systems is discussed. The purpose of the paper is to present several variants of the method that improve its accuracy and convergence in specific problems and to give numerical examples of the improvements. More detailed application to specific spin models is left for subsequent publications.

Geshuo Wang, Zhenning Cai

We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular path integral methodology for spin systems. In particular, the introduction of the inchworm method can significantly suppress the numerical sign problem. Both methods are tweaked to make them work seamlessly with each other. We represent our approach in the language of diagrammatic methods and analyze the asymptotic behavior of the computational cost. Extensive numerical experiments are performed to validate our method.