Interaction-enhanced transport crossover temperature in a Luttinger liquid

Strange metals are highly entangled gapless states of matter that exhibit anomalous transport, such as linear in temperature resistivity, over more than a decade of temperature. Why a single power law should be so robust is an open question. We propose a scenario in which interactions enhance the domain of certain scattering regimes, effectively suppressing other ``would-be regimes." We test this proposal in a one-dimensional Luttinger liquid coupled to a one-dimensional acoustic phonon. We use the memory matrix formalism to calculate the dc electrical and thermal conductivities at low and high temperatures, relative to the Debye cutoff on phonon frequencies, in both the ``clean" (umklapp scattering) and ``dirty" (disorder scattering) limits. We find the crossover temperature separating the low and high temperature regimes to be interaction-dependent, with repulsive interactions substantially increasing it, generally by more than an order of magnitude. This provides a concrete illustration for how interactions can extend a single transport regime over a wider temperature range.