Real space renormalization of Majorana fermions in quantum nano-wire superconductors

TL;DR

This paper uses real space quantum renormalization group methods to analyze topological phase transitions in a one-dimensional p-wave superconductor, highlighting indicators like local compressibility and fidelity.

Contribution

It introduces a novel application of real space renormalization to study topological transitions and Majorana fermions in the Kitaev chain, providing new insights into critical behavior.

Findings

Local compressibility peaks at the critical point.

Ground-state fidelity drops sharply at the transition.

Fidelity susceptibility diverges at the quantum critical point.

Abstract

We have applied the real space quantum renormalization group approach to study the topological quantum phase transition in the one-dimensional chain of a spinless p-wave superconductor. We investigate the behavior of local compressibility and ground-state fidelity of the Kitaev chain. We show that the topological phase transition is signaled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point have been used as a proper indicators for the topological quantum phase transition, which signals the appearance of Majorana fermions. We also present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the topological phase transition.