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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Shannon mutual information of critical quantum cha
ins - Francisco Alcaraz (Universidade de São Paul
o )
DTSTART;TZID=Europe/London:20160111T163000
DTEND;TZID=Europe/London:20160111T173000
UID:TALK64619AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/64619
DESCRIPTION:Associated to the equilibrium Gibbs state of a giv
en critical classical system in d dimensions we c
an associate a special quantum mechanical eigenfu
nction defined in a Hilbert space with the dimensi
on given by the number of configurations of the c
lassical system and components given by the Boltzm
ann weights of the equilibrium probabilities of t
he critical system. This class of eigenfunctions
are generalizations of the Rokhsar-Kivelson\, init
ially proposed for the dimer problem in 2 dimensi
ons. In particular in two dimensions\, where most
of the critical systems are conformal invariant\,
such functions exhibit quite interesting univers
al features. The entanglement entropy of a line of
contiguous variables (classical spins)\, is give
n by the shannon entropy of d=1 quantum chains\,
and the entanglement spectrum of the two dimension
al system are given by the amplitudes of the grou
nd-state eigenfunction of the quantum chain. We p
resent a conjecture showing that the Shannon mutua
l information of the quantum chains in some appro
priate basis (we called conformal basis) show a u
niversal behavior with the size of the line of the
entangled spins (subsystem size). This dependenc
e allow us to identify the conformal charge of the
associated classical critical system (used to de
fine the d=2 quantum eigenfunction) or the quantu
m critical chain. Tests of this conjecture for in
tegrable and non integrable quantum chains will be
presented. We also consider numerical results fo
r two distinct generalizations of the Shannon mutu
al information: the one based in the concept of t
he R\\'\;enyi entropy and the one based on the
R\\'\;enyi divergence. A numerical test of the
extension of this conjecture for critical random
chains (not conformal invariant) is also present
ed. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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