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SUMMARY:Quasiparticle lifetime in a finite conductor and the problem of ma
ny-body localization (Quantum Spacetime Series Seminar)
DTSTART;VALUE=DATE-TIME:20181015T060000Z
DTEND;VALUE=DATE-TIME:20181015T070000Z
DTSTAMP;VALUE=DATE-TIME:20190422T160808Z
UID:indico-event-6667@cern.ch
DESCRIPTION:A quasiparticle in a Landau Fermi liquid has a lifetime that v
aries inversely as the square of its energy. This understanding is ultimat
ely based on a Fermi Golden Rule argument: the decay rate is proportional
to the square of the matrix element for Coulomb interaction of the fermion
s as well as the phase space available to the final products of the decay
process. In a finite conductor\, the single-particle energy levels are dis
crete and the Fermi Golden Rule-based understanding of the quasiparticle l
ifetime is no longer valid when their energies are comparable to the mean
level spacing\, delta. Indeed\, in this regime\, the interparticle interac
tions merely shift these energy levels and the excitation lifetime is infi
nite. A careful analysis shows that the quasiparticle lifetime diverges be
low an energy scale that is parametrically larger than delta. It is instru
ctive to look at this problem from a different perspective. In principle\,
one could diagonalize the interacting many-particle system and the system
\, prepared in any of the eigenstates\, would persist forever in that stat
e. A quasiparticle can always be expressed as a linear superposition of th
e exact many-body eigenstates. If this superposition involves many-body ei
genstates whose energy spread exceeds the quasiparticle energy\, then the
excitation "decays" on a time scale that is inversely proportional to the
energy spread. If the superposition involves a small number of many-body e
igenstates\, then the excitation does not decay. I will show that this tra
nsition is\, in fact\, a many-body localization transition\, i.e.\, an And
erson localization transition in the Fock space of many-body states. I wil
l place this analysis in the context of the problem of quasiparticle lifet
ime in the Kitaev model subjected to integrability-breaking perturbations.
\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6667
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6667
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