Anyon dynamics in field-driven phases of the anisotropic Kitaev model

Abstract

The Kitaev model on a honeycomb lattice with bond-dependent Ising interactions offers an exactly solvable model of a quantum spin liquid (QSL) with gapped $Z_2$ fluxes and gapless linearly dispersing Majorana fermions in the isotropic limit ($K_x=K_y=K_z$). We explore the phase diagram along two axes, an external magnetic field, $h$, applied out-of-plane of the honeycomb, and anisotropic interactions, $K_z$ larger than the other two. For $K_z/K\gg 2$ and $h=0$, the matter Majorana fermions have the largest gap, and the system is described by a gapped $Z_2$ Toric code in which the $Z_2$ fluxes form the low energy bosonic Ising electric (e) and magnetic (m) charges along with their fermionic bound state $\epsilon =e\times m$. In this regime, we find that a small out-of-plane magnetic field creates $\epsilon$ fermions that disperse in fixed one-dimensional directions before the transition to a valence bond solid phase, providing a direct dynamical signature of low energy $Z_2$ Abelian flux excitations separated from the Majorana sector. At lower $K_z$ in the center of the Abelian phase, in a regime we dub the primordial fractionalized (PF) regime, the field generates a hybridization between the $\epsilon$ fermions and the Majorana matter fermions, resulting in a $\psi$ fermion. All the other phases in the field-anisotropy plane are naturally obtained from this primordial soup. We show that in the $Z_2$ Abelian phase, including the PF regime, the dynamical structure factors of local spin flip operators reveal distinct peaks that can be identified as arising from different anyonic excitations. We present in detail their signatures in energy and momentum and propose their identification by inelastic light scattering or inelastic polarized neutron scattering as ``smoking gun" signatures of fractionalization in the QSL phase.

19 pages, 8 figures, 1 table

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• Machine learning reveals features of spinon Fermi surface
• Detection of anyon braiding through pump-probe spectroscopy
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Post-experiment coincidence detection techniques for direct detection of two-body correlations
• Tunable anyonic permeability across ${\mathbb{Z}}_2$ spin liquid junctions
• Hidden subsystem symmetry protected states in competing topological orders