Gapless Visons and Emergent U(1) Spin Liquid in Kitaev's Honeycomb Model*

In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of Ζ₂ spin liquid ground states. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional spin interactions and, in the presence of strong magnetic fields, exhibit no indications of long-range magnetic order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless gauge field resulting in a dense continuum of low-energy states. Such a phase can be naturally understood within the framework of Abrikosov fermionic partons as a U(1) quantum spin liquid with a spinon Fermi surface, emerging via a superconductor-metal transition. Finally, we discuss its stability in the presence of perturbations, Heisenberg and off-diagonal symmetric exchange interactions, that naturally arise in spin-orbit entangled Mott insulators alongside Kitaev interactions.