Interaction-enhanced quantum to classical transport crossover temperature in a Luttinger liquid

TL;DR

This paper investigates how interactions in a Luttinger liquid can extend the temperature range of a single transport regime, explaining the robustness of linear resistivity in strange metals.

Contribution

It demonstrates that interactions significantly increase the crossover temperature in a Luttinger liquid, broadening the regime of anomalous transport.

Findings

Interaction increases crossover temperature by over an order of magnitude.

Memory matrix formalism effectively captures transport in different regimes.

Repulsive interactions notably enhance the temperature range of the transport regime.

Abstract

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.