Quantum interference and spin-charge separation in a disordered Luttinger liquid

TL;DR

This paper investigates how spin-charge separation affects quantum interference and conductivity in a disordered one-dimensional electron system, revealing that spin influences dephasing and localization phenomena.

Contribution

It extends the functional bosonization method to analyze spinful Luttinger liquids with disorder, highlighting the impact of spin-charge separation on quantum interference and dephasing.

Findings

Dephasing length is shorter in spinful LL compared to spinless LL.

Weak localization persists despite spin-charge separation.

Classical memory effects dominate at high temperatures.

Abstract

We study the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of electron-electron interaction and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.