A Study of Interaction Effects and Quantum Berezinskii- Kosterlitz-Thouless Transition in the Kitaev Chain
ABSTRACT :
The physics of the topological state of matter is the second revolution of quantum mechanics. We study the effect of interaction on the topological quantum phase transition and the quantum Berezinskii-Kosterlitz-Thouless (QBKT) transition in topological state of a quantum many-body condensed matter system. We predict a topological quantum phase transition from topological superconducting phase to insulating phase for interacting Kitaev chain. We observe interesting behaviour from the results of renormalization group study on the topological superconducting phase. We derive the renormalization group (RG) equation for QBKT through different routes with a few exact solutions along with the physical explanation, where we find the existence of two new important emergent phases apart from the two conventional phases of this model Hamiltonian. We also present results of length scale dependent study to predict asymptotic freedom like behaviour of the system. This work provides a new perspective on the study of the topological state ofinteracting quantum matter with implication for QBKT.