TITLE: "Entanglement in spin chains".

Luigi Amico
Universita di Catania

ABSTRACT.

We review some of the critical and non critical properties of the
entanglement encoded in the low temperature states of   various one
dimensional quantum  spin models.

At T=0, near  quantum phase transitions,  entanglement can be  
classified in the framework of  the standard scaling theory; however, 
analyzing its range,  profound  differences between   classical 
correlations and non-local correlations  emerge.
At low temperature the   entanglement  sensitivity to thermal and  to
quantum fluctuations obeys   universal $T\neq  0$--scaling behaviour.
We show that the entanglement,  together   with its criticality, 
exhibits a peculiar universal  crossover behaviour.

Far from criticality, we follow up the entanglement in the phenomenon 
leading to the so   called   'separable ground states' in XYZ spin 
systems.  In particular we  evidence that the range of the pairwise 
entanglement  diverges  while  approaching separable ground states, that 
therefore  are reached by a  long range reshuffling of the entanglement 
in the system.
The effect of a finite   temperature in such phenomenon are also
considered.