Absence of Normal Heat Conduction in Strongly Disordered Interacting Quantum Chains

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}

88 pages, 6 figures, v1 ---> v2, The second part of the manuscript (starting from the current section 12) has been substantially rewritten and simplified to improve readability and a few inconsequential errors have been corrected