Abstract
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 superconducting phase to an insulating phase for the 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 explanations, wherein 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 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.
Highlights
IntroductionThe model Hamiltonian of the present problem is below
Introduction of Model Hamiltonian and theRelated Basic PhysicsThe model Hamiltonian of the present problem is below.∑ ∑ H = −t iN=−11(ci†ci+1 + h. c) + ∆ iN=−11(cici+1 + h. c)∑ ∑ +U iN=−11(2ci†ci − 1)(2ci+1†ci+1 − 1) − μ N i ci†ci (1)ci†(ci) is the creation operator
We explore the whole spectrum of renormalization group study of interacting Kitaev model Hamiltonian and we study the quantum Berezinskii-Kosterlitz and Thouless (BKT) (QBKT) for this model Hamiltonian explicitly for different regimes of parameter space
Summary
The model Hamiltonian of the present problem is below. The first term represents the hopping (t) between the nearest-neighbour sites, i.e., kinetic energy contribution of the spinless fermion of the model Hamiltonian. The second term (Δ) represents the p-wave superconducting term, the third term (U) represents the intersite repulsive interaction and μ is the chemical potential. In this model Hamiltonian, there is no on-site repulsion owing to the Pauli exclusion principle. We first recast the model Hamiltonian in terms of Majorana fermion operators to show the deficiency to get a complete picture of topological and trivial state in presence of interactions.
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