Integrals of motion in the many-body localized phase

DOI10.1016/J.NUCLPHYSB.2014.12.014zbMATH Open1328.82034arXiv1406.2175OpenAlexW1990965852WikidataQ62048920 ScholiaQ62048920MaRDI QIDQ901954

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Publication date: 6 January 2016

Published in: (Search for Journal in Brave)

Abstract: We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $0,1$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

Full work available at URL: https://arxiv.org/abs/1406.2175

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