Quasi-one-dimensional Supersolids in Luther-Emery Liquids

The supersolid is a long-sought phase in condensed matter physics, characterized by the coexistence of density wave and superfluid orders. This phase is counterintuitive, as different symmetry-breaking orders typically compete with one another. A deeper understanding of how such a state forms in condensed matter systems remains an open question, especially in quasi-one-dimensional correlated systems. In this work, we investigate the emergence of supersolids in Luttinger-Emery liquids using a variational method. As the system consists of coupled Luttinger-Emery liquid chains, we refer to this phase as a quasi-one-dimensional supersolid. Notably, we demonstrate that the quasi-one-dimensional supersolid phase is energetically favorable in chains with finite size or short-range order. Furthermore, we investigate the collective dynamics of these coexisting charge density waves and superconducting states, identifying a quasi-Goldstone mode. Our theory provides valuable insights into both the ground state and the dynamic properties of supersolids in strongly correlated systems.