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DTSTART:20191027T020000
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DTSTAMP:20210515T012119Z
UID:5b4d8fb08709f429324844@ist.ac.at
DTSTART:20191114T160000
DTEND:20191114T180000
DESCRIPTION:Speaker: Gyorgy Pal Geher\nhosted by Laszlo ErdÃ¶s\nAbstract: I
n this talk we consider the quantum XX spin chain in its ground state and
in the thermodynamic limit. In 2007\, A.R. Its\, B.-Q. Jin and V.E. Korepi
n calculated the asymptotic behaviour of the entanglement entropy of an in
terval of length n (i.e. a block of n consecutive particles) as n tends to
infinity. It is a very natural question what happens if we consider a mor
e complicated subsystem of particles\, for instance\, a union of two inter
vals? In my talk I will present our most recent result on the case when th
e subsystem is such a union\, where the first interval has length m\, the
second has length n\, and the two intervals are separated by a gap of fixe
d length 1. Namely\, we calculate the mutual information between the two i
ntervals as m\,n tend to infinity\, and hence compute the limiting entropy
of the mentioned subsystem. We will see that this problem leads to a rath
er complicated mathematical problem\, namely\, to the estimation of a cert
ain inner product involving a Toeplitz matrix whose symbol possesses Fishe
r-Hartwig singularities. Using techniques from the theory of integrable op
erators we connect this problem first to the famous Fokas-Its-Kitaev Riema
nn-Hilbert problem\, and then to the R-Riemann-Hilbert problem appearing i
n the celebrated 2011 paper of P. Deift\, A.R. Its and I. Krasovsky\, in w
hich they solved the Fisher-Hartwig conjecture.A joint work with A.R. Its\
, V.E. Korepin\, F. Mezzadri\, J. Virtanen.
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, IST Austria
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Mutual information of two intervals in quantum XX spin chain - a Ri
emann-Hilbert approach
URL:https://talks-calendar.app.ist.ac.at/events/2298
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