Absence of Normal Heat Conduction in Strongly Disordered Interacting Quantum Chains

TL;DR

This paper proves that strongly disordered interacting quantum chains exhibit vanishing conductance faster than 1/L, indicating anomalous transport behavior, confirming earlier claims and advancing theoretical understanding.

Contribution

It provides a rigorous proof of anomalous heat conduction in strongly disordered interacting quantum chains, strengthening prior theoretical predictions.

Findings

Conductance vanishes faster than 1/L in disordered chains

Transport is anomalous in strongly disordered quantum systems

Confirms earlier theoretical claims about localization effects

Abstract

We prove that in strongly disordered, interacting, quantum chains, the conductance of a chain of length $L$ vanishes faster than $1/L$. This means that transport is anomalous in such chains. This phenomenon was first claimed in \cite{Basko2006,gornyi2005interacting} and a pioneering treatment appeared in \cite{Imbrie2016a}