Luttinger sum rules in the 2-channel spin 1 Kondo chain

We present numerical results, using the DMRG method, for the zero-temperature phase diagram of the one-dimensional 2-channel Kondo lattice model, coupled to $S=1$ localized spins. Unlike the previously studied 1-channel $S=1/2$ case, the $S=1$ localized spins in the 2-channel model permit a gapped Haldane state, which stabilizes the weak-coupling (``small'' Fermi surface) paramagnetic phase. We focus on the paramagnetic region approaching half-filling, where the interesting possibility has been recently raised of a non-trivial crossover region where the Fermi wavenumber varies continuously.