Emergent ``super-solitons'' following an interaction strength quantum quench across a Luttinger liquid-Mott insulating phase boundary

Rapid progress in cold atom experiments has motivated the study of non-equilibrium many-body dynamics following a sudden deformation of the system Hamiltonian (a ``quantum quench''). Here, we consider the dynamics of localized excitations produced via a quench across a quantum phase boundary separating critical Luttinger liquid and gapped Mott insulating states. Our initial liquid ground state is labeled by a Luttinger interaction parameter $K$, and subject to a density-inhomogeneity forming external potential. For the Mott insulator, we employ the quantum Sine Gordon model at the Luther-Emery (LE) point. We find that over a wide range of initial $K$ values, the quench induces the production of relativistic, non-dispersive traveling density waves, which we dub ``super-solitons.'' The super-solitons are generated from generic antecedent localized density lumps, and appear to be a robust feature of the post-quench dynamics. An isolated exception occurs for the case of $K = K_{LE}$; here, the density dynamics are generically dispersive, and depend sensitively upon the shape of the initial inhomogeneity. We show that the super-solitons do not interact, and we demonstrate that an inhomogeneous Luttinger parameter $K$ can be used to produce super-solitons with different characteristics in the same system.