Localised zero-energy modes in the Kitaev model with vacancy-disorder

TL;DR

This paper investigates how vacancy disorder in the Kitaev model creates localized zero-energy modes, providing analytical descriptions and exploring their potential to probe quantum phase transitions.

Contribution

It introduces analytical forms for vacancy-induced zero modes in the Kitaev model and suggests their use as probes for quantum phase transitions.

Findings

Vacancy disorder induces localized zero modes at defect sites.

Analytical wave functions for these modes are derived in both phases.

The behavior of the IPR and entanglement is analyzed across phases.

Abstract

We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We show that the vacancy disorder induces a zero-mode that is localized at the defect site. We derive analytical forms for these localized wave functions in both the gapped and gapless phases of the Kitaev model. We conjecture that the vacancy disorder can be utilized as a probe of the quantum phase transition (from the gapped to gapless phases) in this model. The behavior of the Inverse Participation Ratio (IPR) in the gapless phase and across the transition is also studied numerically. Comments are made about the behavior of site-site entanglement in the single particle states for the case of a single vacancy.