Abstract
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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Harada, K. (2007). Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application. In: Landau, D.P., Lewis, S.P., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics XVIII. Springer Proceedings in Physics, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32640-3_3
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DOI: https://doi.org/10.1007/978-3-540-32640-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32639-7
Online ISBN: 978-3-540-32640-3
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