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

The Kitaev model on a honeycomb lattice with bond-dependent Ising interactions offers an exactly solvable model of a quantum spin liquid (QSL) with fractionalized excitations: 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 (K-x = K-y = K). For K-z/K >> 2 and h = 0, the matter Majorana fermions have the largest gap, and the system is described by a gapped Z(2) toric code. One of the central questions we address is whether the fractionalized excitations in the different phases have sharp signatures that can be detected in experiments. We show that while the response to single-spin excitations is broad, the spectral function corresponding to two-spin excitations across a bond has sharp signatures that can be attributed to specific anyons. In the toric code regime, the epsilon = e x m fermion, formed from the bosonic Ising electric (e) and magnetic (m) charges, disperses along a specific one-dimensional direction that provides a fingerprint of fractionalization. At lower K-z in the center of the Abelian phase, in a regime we dub the primordial fractionalized regime, the field generates a hybridization between the epsilon fermion and the Majorana matter fermion, resulting in a psi fermion which too has a distinct quasi-one-dimensional dispersion. All the other phases in the field-anisotropy plane are naturally obtained from this primordial soup. These highly constrained fractonlike dispersions can be observable by inelastic light and neutron scattering, thereby providing "smoking gun" signatures of fractionalization in the QSL phase. Our analysis is based on calculations of susceptibilities, topological entanglement entropy, and excitation dynamics, obtained using exact diagonalization and density matrix renormalization group, and supported by perturbation theory.