Doped Kondo chain, a heavy Luttinger liquid

The one dimensional $SU(2)$ Kondo Lattice model is studied by Density Matrix Renormalization Group away from half-filling. We find signatures of a Heavy Tomonaga-Luttinger Liquid (HTLL) phase, which describes one dimensional Heavy Fermions. We compute the wave-vector dependent charge and spin susceptibilities. Our results establish divergent charge and spin correlations at the large Fermi surface $k_F+\pi/2$, and its harmonics. We also find a signature of the hybridization gap at the small Fermi surface. We compare our $N\!=\!2$ results to the large-$N$ Slave Bosons mean field theory of the $SU(N)$ Kondo Lattice model, and find crucial effects of the RKKY interactions on the generation of renormalized effective mass for the $N\!=\!2$ model.