#### 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.

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