Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape

TL;DR

This paper investigates finite-size effects and physical state selection in Kitaev's honeycomb model, analyzing how disorder influences spin excitations and NMR lineshape, with implications for understanding spin liquids and disorder-induced transitions.

Contribution

It clarifies the proper physical state selection in finite-size simulations of the Kitaev model and explores disorder effects on spin excitations and NMR spectra.

Findings

Finite-size effects are significant if the ground state is not fermion-free.

Disorder leads to a transition to a random-flux state.

Calculated NMR lineshape and flux gap distributions in disordered systems.

Abstract

Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static Z_2 gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by Pedrocchi, Chesi, and Loss [Phys. Rev. B 84, 165414 (2011)]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR lineshape. We also predict a transition to a random-flux state with increasing disorder.