We study one-dimensional strongly interacting quantum gas mixtures, including both the Bose-Fermi and spin-$1/2$ Fermi-Fermi mixtures, with weak $p$-wave interaction between intracomponent fermions, and demonstrate that the weak $p$-wave interaction cannot be omitted in the strong interaction region where the strength of $p$-wave interaction is comparable with the inverse of the strength of strongly repulsive $s$-wave interaction. While the total density distribution is not sensitive to the weak $p$-wave interaction, we find that the $p$-wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak $p$-wave interaction, which indicate that a quantum phase transition from an antiferromagnetic state to a ferromagnetic state can be induced by tuning the relative strengths of intracomponent and intercomponent interactions.

• Received 26 November 2015

DOI:https://doi.org/10.1103/PhysRevA.93.033636