Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application

Details Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application

2006-08-03

arxiv.org/abs/cond-mat/0608099v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, 5 figures, Invited talk at the 18th Annual Workshop on Recent Developments of Computer Simulation Studies in Condens

Scientific paper

A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is briefly outlined and a new algorithm using non-binary loops is given for quantum models with high symmetry as SU(N). The algorithm is called non-binary loop algorithm because of non-binary loop updatings. Secondary, one example of our numerical studies using the non-binary loop updating is shown. It is the problem of the ground state of two-dimensional SU(N) anti-ferromagnets. Our numerical study confirms that the ground state in the small N <= 4 case is a magnetic ordered Neel state, but the one in the large N >= 5 case has no magnetic order, and it becomes a dimer state.

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