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.
Stability of the U(1) spin liquid with a spinon Fermi surface in2+1dimensions