UC Riverside

This thesis present the recently theoretical and numerical results on 2D dissipative quantum XY model. The two-dimensional quantum XY model is applicable to the quantum critical properties of several experimental systems, such as superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, and loop current order transition in the cuprates. Renormalization group methods are applied to solve the reformulated ac- tion of the original model in terms of two type topological excitations: vortices and warps. The calculations explain the extraordinary properties of the model studied through quan- tum Monte Carlo simulations: the separability of the correlation function in space and time, the correlation length in space proportional to logarithm of the correlation length in time near the transition from disordered phase to ordered phase. The running dynamical critical exponent is introduced to address the anisotropy between time and space. The effects of anisotropy fields have been examined through renormalization group method. The transi- tion from disordered phase to ordered phase of this model has been studied by quantum Monte Carlo. The divergence of temporal correlation length in function of (Kc − K)/Kc is examined by numerical simulation. The logarithmic relation between temporal correlation length and spacial correlation length is further confirmed. Also, the same logarithmic rela- tion for different correlation function with different space separation is found and implicitly confirmed the separability of correlation function in space and time.