Quantum Critical Dynamics In (2+1) Dimensional U(1) Systems And Phase Transitions Of Superclimbing Dislocation In Crystals

In this thesis,we mainly study three respects of problems in quantum phase tran-sitions:a)Higgs mode near quantum critical point;b)quantum transport properties at superfluid-Mott insulator phase transition;c)phase transitions in superclimbing dis-location with a Coulomb-type interaction between jos in crystal.In the former two problems,we investigate the quantum critical dynamics in(2 + 1)-dimensional U(1)systems,such as Bose Hubbard model and J-current model.As for the last problem,we study the edge dislocations which can perform superclimb,and the specific model can be derived by coupling the classical string model for the dislocations with the superfluid model which describes the superflow along the dislocation core.In our work,we apply worm algorithm to simulate these models by Monte Carlo method.a)In simulation,we measure the kinetic energy correlation in Matsubara frequen-cies,and by applying analytic continuation,we obtain the spectral function correspond-ing to the response function to kinetic energy.Then,we calculate the universal spectral function near the quantum phase transition point,and find that there exists a resonance peak for Higgs mode.Surprisingly,we also find a resonance peak with the similar structure in Mott insulator phase and even in normal liquid.The underlying mechanism of this counterintuitive phenomenon has not been understood yet.Besides,in order to investigate the Higgs mode in ultracold atom experiments,we also apply Monte Carlo simulations and the first principle approach to calculate the temperature shift of the sys-tem subject to a modulation of the lattice depth in optical lattice.By directly comparing the obtained data with the result of the experiment in Ref.[1],we find that they are consistent.Based on this,we also discuss the conditions and proposals for experiment to detect the Higgs resonance peak.b)we calculate the universal conductivity depending on Matsubara frequencies at a high accuracy in(2+ 1)dimensional XY universality class and for the first time,the data for the universal conductivity are so precise that a reliable check of the transport theory based on AdS/CFT correspondence hypothesis proposed in Ref.[2]becomes possible.We find that this theory can not fit our data,unless a rescaling factor is in-cluded in the temperature of the black brane.In addition,we propose a new classical model extended from standard J-current model.This model allows us largely eliminate finite temperature corrections by tuning its parameters,and thus making us obtain the universal conductivity of much more accuracy for the same simulation time.Further-more,according to these more precise data,we check another newly proposed transport theory which is also based on AdS/CFT correspondence,and we find that the theoretical result is perfectly consistent with our data.Finally,we also investigate the requirements for measuring the universal conductivity in a ultracold atom experiment,and propose a practical scheme to realize it.c)We mainly study the quantum behavior of a tilted edge dislocation which can superclimb in the extra atom plane.We find that the elastic long-range interactions between jogs do not affect the phase diagram qualitatively,and their main role is reduced to the renormalization of the strength of local interactions.We also find that Gaussian approximation could well describe the quantum rough phase of the dislocation.