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arXiv:1606.04700 · Physical review. B./Physical review. B

Decay of density waves in coupled one-dimensional many-body-localized systems

Peter Prelovšek

Published Oct 10, 2016• 8 citations
arXivHTMLPDF

Abstract

This work analyzes the behavior of coupled disordered one-dimensional systems as modelled by identical fermionic Hubbard chains with the on-site potential disorder and coupling emerging through the interchain hopping ${t}^{\ensuremath{'}}$. The study is motivated by the experiment on fermionic cold atoms on a disordered lattice, where a decay rate of the quenched density wave was measured. We present a derivation of the decay rate $\mathrm{\ensuremath{\Gamma}}$ within perturbation theory and show that, even at large disorder along the chains, the interaction leads to finite $\mathrm{\ensuremath{\Gamma}}>0$, the mechanism being the interaction-induced coupling of in-chain localized and interchain extended single-fermion states. Explicit expressions for $\mathrm{\ensuremath{\Gamma}}$ are presented for a weak interaction $U<t,{t}^{\ensuremath{'}}$, but extended also to the regime $t>U>{t}^{\ensuremath{'}}$. It is shown that, in both regimes, $\mathrm{\ensuremath{\Gamma}}$ increases with the interchain hopping ${t}^{\ensuremath{'}}$, as well as decreases with increasing disorder.

DOI
10.1103/physrevb.94.144204

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