Abstract
In this thesis, we are going to discuss various aspects of one-dimensional correlated electron systems. More specifically, in chapter one, we introduce some basic knoweledge about one dimensional quantum spin chains and Hubbard model. In chapter two, we discuss a model of one-dimensional dopped Mott insulator from the point of view of slave fermion gauge theory, where we found that the interplay between hole motion and spin fluctuation consitute an interesting realization of confinement physics in gauge theory. In chapter three, we discuss the effect of an external magnetic field induced quantum phase transition in a one-dimensional spin liquid with orbital degrees of freedom. Moreover, from the renormalization group studies, we found that there is a symmetry restoration toward a SO(4) point, then using the form factor technique for the integrable SO(4) Gross-Neveu model, we are able to calculate various correlation functions of this model. In the final cahpter, we study the boundary critical phenomenon induced by a local impurity embedded in a critical quantum spin chain where the bulk critical theory is described by a SU(2)$_2$ Wess-Zumino-Novikov-Witten model. Through the combination of bosonization, renormalization group and boundary conformal field theory analysis, we found that the generic boundary fixed point for an internal impurity is either an open chain or a periodic chain. For a Kondo impurity, through identifying the leading irrelevant operators, we show that two-channel Kondo fixed point can be realized in our model.