For distribution

[CM ICTP - Trieste]

SEMINAR on   Disorder and strong electron correlations



Thursday, 12 April   -    11:00 a.m.



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



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



"Ellipse of constant entropy in the XY spin chain"

Abstract

	We study the bi-partite entanglement in the ground state of the 
one-dimensional XY spin 1/2 model, by calculating the Von Neumann 
Entropy of a block of neighboring spins.  We consider the 
double-scaling limit in which the block size is much bigger than unity, 
but still much smaller than the length of the whole chain.  As long as 
the system is gapped, as the size of the block increases toward 
infinity, the entropy reaches a finite saturation value. We study this 
limit entropy in the two-dimensional phase diagram of the system, as a 
function of the anisotropy parameter and of the external magnetic 
field.  We identify its minima at product states and its divergences at 
the quantum phase transitions. We find that the curves of constant 
entropy are ellipses and hyperbolae and that they all meet at one point 
(it essential critical point).  The entropy is highly discontinuous 
across this point: depending on the direction of approach to the 
essential critical point the entropy can take any value on the positive 
real axis.  In the vicinity of this point small changes in the 
parameters cause drastic changes of the entropy and this can be really 
important for quantum control.  Finally, I will present some more 
technical results from a work in progress, in which a second, 
degenerate, ground state of the model is identified and I'll briefly 
discuss its meaning and significance.