Numerical study of gauge theories and its application to quantum many-body phenomena

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In the present study, we investigate phase diagrams of various quantum many-body systems including strongly-correlated electron systems and multi-species ultra-cold atomic gases on an optical lattice. By varying parameters of the models, a phase transition takes place and low-energy excitations in each phase are investigated by the gauge theory, which is most important theory in elementary particle theory. Besides analytical study, we use the numerical study including Monte-Carlo simulations and numerical inveatigation of the Gross-Pitaevskiiand/or Gintzburg-Landau equations describing superfluid and superconductivity. We particularly focus on systems of ultra-cold atomic gases on an optical lattice, which are quite controllable. Numerical Monte-Carlo experiments reveals various interesting properties of these systems.