Majorana Fermi surface state in a network of quantum spin chains

We use junctions of critical spin-1 chains as the basic elements to construct a honeycomb network that harbors a gapless chiral spin liquid phase. The low-energy modes are described by spin-1 Majorana fermions that form a two-dimensional Fermi surface when the interactions at the junctions are tuned to the vicinity of chiral fixed points with staggered chirality. We discuss the physical properties and the stability of this chiral spin liquid phase against perturbations from the point of view of the effective field theory for the network. We find clear connections with the excitation spectrum obtained in parton constructions on the kagome lattice.