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

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.

7 pages, 9 figures; to appear in Journal of the Physical Society of Japan (JPSJ)

References in corpus (14)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Probing Atomic Structure and Majorana Wavefunctions in Mono-Atomic Fe-chains on Superconducting Pb-Surface
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• Topology induced anomalous defect production by crossing a quantum critical point
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Gapped Quantum Criticality Gains Long Time Quantum Correlations
• Compressibility as a probe of quantum phase transitions in topological superconductors

Cited by in corpus (3)

• Exact phase diagram and topological phase transitions of the XYZ spin chain
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube