Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

TL;DR

This paper develops a bosonization-fermionization approach to analyze the density-density propagator in one-dimensional spinless fermions with non-linear dispersion, and calculates the Coulomb drag resistivity showing a quadratic temperature dependence.

Contribution

It introduces a novel expansion for the density-density propagator using irrelevant quasiparticle interactions in a non-linear dispersion model.

Findings

Coulomb drag resistivity scales as T^2 for both free and interacting fermions.

In-chain repulsive interaction reduces the resistivity compared to the non-interacting case.

Quasiparticle interaction contributes a T^4 correction to the resistivity at low temperatures.

Abstract

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.