  Measurements of the low-temperature thermal conductivity collected on
insulators with geometrical frustration produce important experimental facts
shedding light on the nature of quantum spin liquid composed of spinons. We
employ a model of strongly correlated quantum spin liquid located near the
fermion condensation phase transition to analyze the exciting measurements of
the low-temperature thermal conductivity in magnetic fields collected on the
organic insulators EtMe3Sb[Pd(dmit)_2]2 and \kappa-(BEDT-TTF)2Cu2(CN)3. Our
analysis of the conductivity allows us to reveal a strong dependence of the
effective mass of spinons on magnetic fields, to detect a scaling behavior of
the conductivity, and to relate it to both the spin-lattice relaxation rate and
the magnetoresistivity. Our calculations and observations are in a good
agreement with experimental data.
