Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Significance In a quantum spin liquid, the spins remain disordered down to zero temperature, and yet, it displays topological order that is stable against local perturbations. The Kitaev model with anisotropic interactions on the bonds of a honeycomb lattice is a paradigmatic model for a quantum spin liquid. We explore the effects of a magnetic field and discover an intermediate gapless spin liquid sandwiched between the known gapped Kitaev spin liquid and a polarized phase. We show that the gapless spin liquid harbors fractionalized neutral fermionic excitations, dubbed spinons, that remarkably form a Fermi surface in a charge insulator. The Kitaev model with an applied magnetic field in the H∥[111] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at Hc1≃0.2K and a second transition at a higher field Hc2≃0.35K to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function S(k) and the Fermi surface ϵFS(k) of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.