Numerical study of quantum frustrated systems by tensor network methods

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We construct a new MERA tensor network based on entanglement renormalization for quantum triangular lattice models. We apply it to the ground state of an S = 1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice. Magnetic ground states are numerically confirmed in the weak anisotropic region. The magnetic structure is spiral with an incommensurate wave vector that is different from the classical one. We also develop a Bayesian method for the scaling analysis of critical systems, and a non-local unitary transformation for removing the negative sign problem in SO(N)bilinear-biquadratic chains. We also confirm the systematic shift of universality class to a weak first-order transition from large-scale quantum Monte Carlo calculations of two-dimensional SU(N) JQ models.