Exploring the unconventional continuous phase transition between unrelated symmetry breaking phases

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Continuous phase transition is a well-known phenomena and, in general, it can be explained by the Landau-Ginzburg-Wilson paradigm. In order to explore numerically another new type of continuous phase transition in quantum systems, we first studied new quantum Monte Carlo algorithms for high performance samplings. Using those high performance algorithms, we have done large-scale quantum Monte Carlo simulations for the quasi-one-dimensional SU(N) quantum models and we found the possibility of continuous quantum phase transitions between valence-bond-solid state and SU(N) symmetry breaking state for the N=3 and 4 cases. Each of them is not a symmetry breaking state of other one.