Charge density wave and vanishing drude weight in a one dimensional Kondo model

We propose to simulate Kondo transition in a bilayer optical lattice with a displacement field

between the two layers. We derive a Kondo model for this set up and then study its phase diagram

in one dimension by tuning the Kondo coupling JK through the density matrix renormalization group

(DMRG) calculation. At small JK , the ground state is a Luther-Emery liquid which can be viewed

as a descendant from a fractional Luttinger liquid. At large JK , the model hosts a conventional

Luttinger liquid as an analog of the heavy Fermi liquid in higher dimension. Surprisingly, we find

that both the Luttinger parameter Kc and the velocity υc have a dip at intermediate regime between

the above two phases. For commensurate filling, the intermediate regime is always replaced with

a charge density wave ordered insulator due to the small Luttinger parameter. When the filling

approaches incommensurate, the charge density wave ordered phase shrinks. In this case, we find

that the Luttinger parameter, the charge velocity and thus the drude weight in optical conductivity

vanish within numerical error. Vanishing drude weight has been argued to be a necessary condition

for the strange metal phases observed in higher dimension. Our work shows that this is possible

even in a translationally invariant one dimensional model at incommensurate filling