# Thermal Transport in One Dimensional Electronic Fluid

## TL;DR

This paper investigates thermal conductivity in a one-dimensional electronic fluid, revealing ballistic heat propagation at short times and fractional scaling laws at low frequencies and large scales due to Levy flights of bosons.

## Contribution

It introduces a novel framework partitioning the many-body Hilbert space into bosonic and fermionic sectors, elucidating their roles in thermal transport and uncovering fractional scaling behavior.

## Key findings

- Ballistic heat propagation at short timescales.
- Fractional scaling laws $\, ext{(}\omega^{-rac{1}{3}} ext{)}$ and $L^{1/3}$ at low frequencies and large sizes.
- Thermal transport dominated by Levy flights of low-momentum bosons.

## Abstract

We study thermal conductivity for one-dimensional electronic fluid. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than bosonic Umklapp time, the momentum of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to $T / i\omega$. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by L{\'e}vy flights of low-momentum bosons that lead to a fractional scaling, $\omega^{-\frac{1}{3}}$ and $L^{1/3}$, of heat conductivity with the frequency $\omega$ and system size $L$ respectively.