Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder

Abstract

Kitaev's model of spins interacting on a honeycomb lattice describes a quantum spin-liquid, where an emergent static ${\mathbb{Z}}_2$ gauge field is coupled to Majorana fermions. In the presence of an external magnetic field and for a range of interaction strengths, the system behaves as a gapped, non-Abelian quantum spin-liquid. In this phase, the vortex excitations of the emergent ${\mathbb{Z}}_2$ gauge field have Majorana zero modes bound to them. Motivated by recent experimental progress in measuring and characterizing real materials that could exhibit spin-liquid behavior, we analytically calculate the dynamical spin structure factor in the non-Abelian phase of the Kitaev's honeycomb model. In particular, we treat the case of quenched disorder in the vortex configurations. Our calculations reveal a peak in the low-energy dynamical structure factor that is a signature of the spin-liquid behavior. We map the effective Hamiltonian to that of a chiral p-wave superconductor by using the Jordan-Wigner transformation. Subsequently, we analytically calculate the wave functions of the Majorana zero modes, the energy splitting for finite separation of the vortices and finally, the dynamical structure factor in presence of quenched disorder.

arXiv comment13 pages, 6 figures

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• Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid
• Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model
• Geometric description of the Kitaev honeycomb lattice model
• Exceptional dynamics of interacting spin liquids
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Response to glassy disorder in coin on spread of quantum walker
• Realizing Majorana fermion modes in the Kitaev model
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands