  Highly frustrated spin systems such as the kagome lattice (KL) are a treasure
trove of new quantum states with large entanglements. We thus study the
spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain (KSC), which is
one-dimensional KL, using the density-matrix renormalization group (DMRG)
method. Calculating central charge and entanglement spectrum for the KSC, we
find a novel gapless spin liquid state with doubly degenerate entanglement
spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying
continuum in the dynamic spin structure calculated by dynamical DMRG method. We
propose a resonating dimer-monomer liquid state that would meet these features.
