Quantum Monte Carlo Study on Strongly Quantum Fluctuated Systems

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Systems with strong quantum fluctuation due to the stracture of lattice in order to find new peculiar properties.The effects due to the structure of the lattice on the ordering configuration in the Heisenberg antiferromagnets are investigated. Ordering configuration means the configuration of singlet bonds which is classified with the VBS picture. In particular we investigated a chain which consists of two of S=1 spins and two of S=1/2 spins.We also investigated effects of inhomogeneity on quantum mechanical order : effects of impurities of S=1/2 spins, and effects of dilution on the lader lattice and square lattice. In the latter project, we find so-called quantum Criffiths phase where the any correlation in the spatial direction decays exponentially but the correlation in the time axis diverges. This divergence causes the divergence of the local susceptibility.We studied a new phase due to the quantum fluctuation in the magnetization curve in the ground state of antiferromagnetic Heisenberg model with XY anisotropy. There a collinear configuration which is unfavorite in classical case becomes stable. The transition is clearly observed by investigating the wavefunction although the transition is not clear in the changes of physical quantities.We investigated the low temperature properties of quantum spin systems by quantum Monte Carlo method and transfer matrix method.We found a new mechanism of the ferromagnetism in the Hubbard model and analyzed the nature of the ferromagnetism.We started to study the dynamics of system where the quantum fluctuation has a dominant role.