Primordial fractionalized phase in the anisotropic Kitaev model in a field and testable predictions for fractionalized excitations*

We report the discovery of a rich phase diagram for two-dimensional quantum spin liquids (QSL) with anisotropic spin interactions in a field. The Kitaev model with bond dependent Ising interactions on a honeycomb lattice offers an exactly solvable model for Z2 quantum spin liquids with gapped fluxes and gapless linearly dispersing majorana fermions for isotropic coupling. The majorana fermions get gapped out in the anisotropic Toric code limit when one of the coupling strengths is much larger than the other two, leading to a gapped Z2 QSL, where the fluxes form the low energy excitations– bosonic Ising electric (e) and magnetic (m) charges and the composite fermion ε=exm. The effect of an external magnetic field h in the [111] direction is remarkably different on the gapless and the gapped Z2 QSL that stems from the difference in the nature of excitations in the two QSLs. While the former shows transitions to a gapped chiral QSL and a gapless U(1) QSL before the polarized paramagnet sets in, the latter gives way to a valence bond solid (VBS) phase with dimers on stronger bonds. The key to understanding this rich phenomenology is the Zeeman-field-induced hybridization between the gauge ε and majorana fermions resulting in a matter-gauge coupled gapped Z2 QSL at intermediate magnetic field and anisotropy – dubbed the Primordial Fractionalized (PF) phase. All the other phases in the field-anisotropy plane are naturally obtained from this primodial soup, highlighting the importance of our discovery. The momentum-dependent dynamical spin structure factor shows distinct signatures of fractionalization and the evolution of the multiple peaks as a function of the magnetic field allow us to make testable predictions for experiments.