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Integrals of motion in the many-body localized phase

Jun 9, 2014

46 pages

Published in:

Nucl.Phys.B 891 (2015) 420-465,
Nucl.Phys.B 900 (2015) 446-448 (erratum)

Published: Dec 13, 2014

e-Print:

1406.2175 [cond-mat.dis-nn]

DOI:

10.1016/j.nuclphysb.2014.12.014,
10.1016/j.nuclphysb.2015.09.017 (erratum)

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Abstract: (Elsevier)

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.

Note:

65 pages, 12 figures. Corrected typos, added references

71.30.+h
73.20.Fz

References(50)

Figures(0)

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