Large violation of Wiedemann Franz law in Luttinger liquids

TL;DR

This paper demonstrates that in weakly disordered Luttinger liquids near commensurate filling, the Wiedemann-Franz law can be strongly violated, with the Lorenz number deviating significantly from Fermi liquid predictions due to Umklapp scattering effects.

Contribution

It reveals a regime where the Lorenz number drastically deviates from the WF law in Luttinger liquids, highlighting the role of approximate symmetries and scattering rates.

Findings

Lorenz number L can be much larger than 1 near commensurate filling.

L can be much smaller than 1 in slightly doped systems.

Strong deviation from WF law due to Umklapp scattering effects.

Abstract

We show that in weakly disordered Luttinger liquids close to a commensurate filling the ratio of thermal conductivity kappa and electrical conductivity sigma can deviate strongly from the Wiedemann Franz (WF) law valid for Fermi liquids scattering from impurities. In the regime where the Umklapp scattering rate Gamma_U is much larger than the impurity scattering rate Gamma_imp, the Lorenz number L = (kappa/sigma T) rapidly changes from very large values, L ~ (Gamma_U/Gamma_imp) >> 1 at the commensurate point to very small values, L ~ (Gamma_imp/Gamma_U) << 1 for a slightly doped system. This surprising behavior is a consequence of approximate symmetries existing even in the presence of strong Umklapp scattering.