Alladi Ramakrishnan Hall

A Study of Interaction Effects and Quantum Berezinskii- Kosterlitz-Thouless Transition in the Kitaev Chain

Sujit Sarkar

Poornaprajna Institute of Scientific Research

The physics of the topological state of matter is the second revolution in quantum mechanics.
We study the effect of interactions 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 su-
perconducting phase to an insulating phase for the interacting Kitaev chain. We observe interest-
ing 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 explanations, wherein we find the existence of
two new important emergent phases apart from the two conventional phases of this model Hamil-
tonian. We also present results of a length-scale dependent study to predict asymptotic freedom
like behaviour of the system. We do rigorous quantum field theoretical renormalization group
calculations to solve this problem.