Quantum spin metal state on a decorated honeycomb lattice

We present a modification of exactly solvable spin-(1/2) Kitaev model on the decorated honeycomb lattice, with a ground state of ``spin metal'' type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi-circle those size depends on the ratio of exchange couplings. Low-temperature heat capacity $C(T)$ and dynamic spin susceptibility $\chi(\omega,T)$ are calculated in the case of small Fermi-circle. Whereas $C(T)\sim T$ at low temperatures as it is expected for a Fermi-liquid, spin excitations are gapful and $\chi(\omega,T)$ demonstrate unusual behavior with a power-law peak near the resonance frequency. The corresponding exponent as well as the peak shape are calculated.