For certain crystalline systems, most notably the organic compound EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$, experimental evidence has accumulated of an insulating state with a high density of gapless neutral excitations that produce Fermi-liquid-like power laws in thermodynamic quantities and thermal transport. This has been taken as evidence of a fractionalized spin-liquid state. In this Rapid Communication, we argue that if the experiments are taken at face value, the most promising spin-liquid candidates are a $Z_4$ spin liquid with a spinon-Fermi surface and no broken symmetries, or a $Z_2$ spin liquid with a spinon-Fermi surface and at least one of the following spontaneously broken: (a) time-reversal and inversion, (b) translation, or (c) certain point-group symmetries. We present a solvable model on the triangular lattice with an (a) type $Z_2$ spin-liquid ground state.

• Received 31 August 2012

DOI:https://doi.org/10.1103/PhysRevB.87.140402