We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion ...used in Molecular Dynamics, these algorithms are based on the Suzuki-Trotter decomposition of exponential operators and unlike more commonly used algorithms exactly conserve spin length and, in special cases, energy. Using higher order decompositions we investigate integration schemes of up to fourth order and compare them to a well-established fourth order predictor-corrector method. We demonstrate that these methods can be used with much larger time steps than the predictor-corrector method and thus may lead to a substantial speedup of computer simulations of the dynamical behavior of magnetic materials.
Using a recently implemented integration method Krech et al. based on an iterative second-order Suzuki–Trotter decomposition scheme, we have performed spin dynamics simulations to study the critical ...dynamics of the BCC Heisenberg antiferromagnet with uniaxial anisotropy. This technique allowed us to probe the narrow asymptotic critical region of the model and estimate the dynamic critical exponent
z=2.25±0.08. Comparisons with competing theories and experimental results are presented.
We have studied numerically exact auxiliary field quantum Monte Carlo scheme for the spin and orbital rotational invariant Hamiltonian by combining series expansion and Trotter decomposition. We have ...used algorithm to solve the dynamical field theory equations. We have employed Boltzmann operator with respect to the total interaction. The method significantly relaxes the sign problem and allows in principle for more than two orbitals. The computational effort increases with the perturbation orders appearing in the Mote Carlo samples. The order become very large in multiorbital systems. To remove this difficulty we have used the Hirsch-Fye quantum Monte Carlo and parturbation series expansion quantum Monte Carlo methods. This algorithm enabled us not only to handle three or more orbitals but also to reach much stronger coupling than in Hirsch-Fye quantum Monte Carlo calculations, even for the two orbital Hubbard model.
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