Site dilution in Kitaev's honeycomb model

TL;DR

This paper investigates how site dilution affects Kitaev's honeycomb model, revealing flux binding, local moments, and altered thermodynamics, with distinct behaviors in gapped and gapless phases.

Contribution

It introduces the effects of vacancies in the Kitaev model, showing flux binding, local moments, and their interactions, along with a mapping to a bipartite random hopping problem for disordered phases.

Findings

Vacancies bind fluxes and induce local moments.

Susceptibility in the gapless phase depends logarithmically on field strength.

Disorder leads to a Dyson-type singularity in the density of states.

Abstract

We study the physical consequences of site dilution in Kitaev's honeycomb model, in both its gapped and gapless phases. We show that a vacancy binds a flux of the emergent $Z_2$ gauge field and induces a local moment. In the gapped phase this moment is free while in the gapless phase the susceptibility has the dependence $\chi(h)\sim\ln(1/h)$ on field strength $h$. Vacancy moments have interactions that depend on their separation, their relative sublattice, and the phase of the model. Strikingly, in the gapless phase, two nearby vacancies on the same sublattice have a parametrically larger $\chi(h)\sim(h[\ln(1/h)]^{3/2})^{-1}$. In the gapped phase, even a finite density of randomly distributed vacancies remains tractable, via a mapping to a bipartite random hopping problem. This leads to a strong disorder form of the low-energy thermodynamics, with a Dyson-type singularity in the density of states for excitations.