  The unusual ground state and thermodynamic properties of spin-1/2 two-leg
honeycomb (HC) spin ladder are systematically studied by jointly utilizing
various analytical and numerical methods. The HC spin ladder is found to
exhibit behaviors dramatically different from those of the conventional square
spin ladder. A strong relevant term nJ and a half saturation magnetization
plateau that can be attributed to the formation of diluted dimer states are
observed in the HC ladder, both of which are absent in the square ladder. The
ground state phase diagram of the HC spin ladder is identified, and the
thermodynamic properties of the specific heat and susceptibility for different
couplings are thoroughly explored, where two kinds of excitations are unveiled.
The distinct Wilson ratios for both spin ladders at the lower critical fields
are also obtained. Our calculated result is well fitted to the experimental
data of the two-leg HC spin ladder compound [Cu2L1(N3)4]n.
