Thurs seminar

[ICTP info point]

CONDENSED MATTER AND STATISTICAL PHYSICS SECTION
	
INFORMAL SEMINAR on

Disorder and strong electron correlations




Thursday, 30 November    -    11:00 a.m.




Lecture Room 'C',  Main Bldg.- terrace level



F. FRANCHINI  ( The Abdus Salam I.C.T.P. )



" The emptiness formation probability: Going beyond the Luttinger 
liquid model "


Abstract

The Emptiness Formation Probability (EFP) is a very important 
correlation function in the theory of integrable models.  In 
One-Dimension, it measures the probability that a region of length n 
will present no particles.  For spin chains, the Jordan-Wigner 
transformation maps the EFP into the Probability of Formation of 
Ferromagnetic Strings (PFFS), i.e. the probability that a string of n 
spins are all aligned in one direction.  The configuration measured by 
the EFP is in general very different from the equilibrium one.  Because 
of this, the EFP is an ideal example of a correlator that cannot be 
captured by a bosonization approach, since it requires contributions 
from the whole spectrum of the system.  In the first part of the talk,  
we will present an alternative (exact) way to calculate the EFP for the 
anisotropic XY model at zero temperature, by representing this 
correlator as the determinant of a Toeplitz matrix.  Using the 
literature on Toeplitz determinants, we will be able to calculate the 
asymptotic behavior of the EFP in the different regions of the phase 
diagram of the XY model.  In the second part of the talk, we will 
introduce a hydrodynamic description of integrable models at zero 
temperature, that will allow us to calculate the EFP for simple 
systems.  This hydrodynamic approach is a collective description of the 
system that takes naturally into account the curvature of the spectrum, 
at the cost of dealing with a non-linear theory.  This approach could 
be used to describe other effects beyond the Luttinger Liquid model, 
for instance the higher energy corrections to the exact Spin-Charge 
separation prediction for low-lying excitations.