Abstract
We describe a family of one-dimensional (1D) liquids, which we call ``staggered liquids,'' in the phase diagram of the 1D Kondo-Heisenberg model. It encompasses three distinct spin-gapped liquids and a Luttinger liquid (LL) phase. A staggered liquid is characterized by gapless modes with a large Fermi-sea signature in the charge-density wave (CDW) mode, and the superconducting order involves the near condensation of charge-$2e$ Cooper pairs with finite center-of-mass momentum. In particular, the conventional gapless ${2k}_{F}$ CDW and $k=0$ pairing modes are absent. We analytically derive the phase transition from an intermediate-coupling spin-gap phase to the strong-coupling gapless LL phase of the Kondo-Heisenberg lattice model.
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