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UID:0-785@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20211214T110000
DTEND;TZID=Europe/Paris:20211214T120000
DTSTAMP:20211207T132617Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
s-marco-tarzia-lptmc-2/
SUMMARY:Séminaire du LPTMS : Marco Tarzia (LPTMC) - Petit amphi\, bâtimen
t Pascal n° 530 - 14 Déc 21 11:00
DESCRIPTION:Fully localized and partially delocalized but non-ergodic state
s in the tails of critical Erdos-Renyi graphs\nMarco Tarzia (Laboratoire d
e Physique Théorique de la Matière Condensée)\nOnsite seminar + zoom (I
D: 933 8982 7691\, PW: V75fAY\, link:\nhttps://cnrs.zoom.us/j/93389827691
?pwd=eGtrLzg0eDJZdGdUR1ZuWEhsRnlhQT09).\n\nIn this talk I will discuss th
e spectral properties of the adjacency matrix of critical Erdos-Renyi grap
hs\, i.e. when the average degree is of order log N. In a series of recent
inspiring papers Alt\, Ducatez\, and Knowles have rigorously shown that t
hese systems exhibit a "semilocalized" phase in the tails of the spectrum
where the eigenvectors are exponentially localized on a sub-extensive fra
ction of nodes with anomalously large degree. We propose two approximate
analytical strategies to analyze this regime based respectively on the si
mple "rules of thumb" for localization and ergodicity and on an approximat
e treatment of the self-consistent cavity equation for the resolvent. Both
approaches suggest that the tails of the spectrum split in two different
phases: a fully Anderson localized phase at the spectral edges\, in which
the eigenvectors are localized around a unique center\, and an intermediat
e partially delocalized but non-ergodic phase\, where the eigenvectors spr
ead over many resonant localization centers. In this phase the exponential
decay of the effective tunneling amplitudes between the localization cent
ers is counterbalanced by the large number of nodes towards which tunnelin
g can occur\, and the system exhibits mini-bands in the local spectrum ove
r which the Wigner-Dyson statistics establishes. We complement these resul
ts by a detailed numerical study of the finite-size scaling behavior of s
everal observables that fully supports the theoretical predictions and all
ows us to determine the critical properties of the two transitions. Critic
al Erdos-Renyi graphs provide a pictorial representation of the Hilbert
space of a generic many-body Hamiltonian with short range interaction. In
particular we argue that their phase diagram can be mapped onto the out-of
-equilibrium phase diagram of the quantum random energy model.
CATEGORIES:seminars
LOCATION:Petit amphi\, bâtiment Pascal n° 530\, rue André Rivière\, Ors
ay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Rivière\, Orsay
\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Petit amphi\, bâtiment Pasca
l n° 530:geo:0,0
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