Hydrodynamic descriptions of multi-component quantum fluids in one-dimensional systems

Hydrodynamic theories have been widely used in studying the transport problem of interacting electronic systems with minimal momentum relaxation. A strongly interacting plasma of linearly dispersing electron and hole excitations, also known as a Dirac fluid, can be captured by relativistic hydrodynamics. The most studied example of a Dirac fluid is two-dimensional graphene at charge neutrality, which in the absence of impurities has diverging thermal conductivity but finite electric conductivity, leading to violations of the Wiedemann-Franz law. It is natural to ask which quantum liquids in one dimension, where additional non-pertubative methods are available, can possess similar transport properties to charge-neutral graphene, and what the leading corrections to this behavior are in realistic systems. In this work, within the frame of hydrodynamics, we investigate a generic Luttinger liquid theory (i.e., incorporating integrability-breaking perturbations) which is closely related to the two-dimensional Dirac fluid in graphene, with various transport properties calculated.