Renormalization group study on strongly correlated system

Abstract

In condensed matter systems, we cannot use the quantum field theory in general because we need to consider the lattice structures. However, near the quantum critical point, since the correlation length becomes divergent, we can consider the system as continuum and we can use the quantum field theory. Also, we can observe the scale invariance near the quantum critical point, so, the renormalization group methods using these properties are used to study the low-energy behaviors near the quantum phase transition in the several strongly correlated systems. In this thesis, I have studied unconventional universality classes in strongly correlated system by using the renormalization group methods.