14. Nov 2019
Mutual information of two intervals in quantum XX spin chain – a Riemann-Hilbert approach
Datum: 14. November 2019 |
Sprecher: Gyorgy Pal Geher, University of Reading, UK
Veranstaltungsort: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
In my talk I will present our most recent result on the case when the 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 fixed length 1. Namely, we calculate the mutual information between the two intervals 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 rather complicated mathematical problem, namely, to the estimation of a certain inner product involving a Toeplitz matrix whose symbol possesses Fisher-Hartwig singularities. Using techniques from the theory of integrable operators we connect this problem first to the famous Fokas-Its-Kitaev Riemann-Hilbert problem, and then to the R-Riemann-Hilbert problem appearing in the celebrated 2011 paper of P. Deift, A.R. Its and I. Krasovsky, in which they solved the Fisher-Hartwig conjecture.
A joint work with A.R. Its, V.E. Korepin, F. Mezzadri, J. Virtanen.