Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice

We study the one-dimensional two-channel Kondo lattice model using density matrix renormalization group method. Extending the earlier work (Schauerte et. al., PRL 94:147201, 2005), we show that algebraic hastatic density wave order appears generically for strong coupling, leading to a rich phase diagram fundamentally different from the one-dimensional single-channel Kondo lattice. The hastatic phases are metallic away from quarter filling and we show that they correspond to different heavy Tomonaga-Luttinger liquids with Fermi surface wave-vectors unrelated to light or heavy wave-vectors in the single-channel Kondo case. Numerical results are compared with large-N mean-field predictions and an additional vectorial order parameter associated with hastatic order is detected which we ascribe to the unique spinorial nature of the order.