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Scientific Report 2007-2009<br />
Condensed matter physics and biophysics<br />
C44. Quantum statistical mechanics and quantum information<br />
The interest is in the quantum information (QI) properties<br />
of systems currently studied in quantum statistical<br />
mechanics like superfluids, itinerant magnetic and spin<br />
systems.<br />
Some typical features of many-body theory, like the<br />
large-size limit, spontaneous symmetry breaking mechanisms<br />
and the mean field approximation need to be reconsidered<br />
from the point of view of a quantum information<br />
properties.<br />
The obvious finite size of physical systems considered<br />
in QI is a difficulty not only from the point of view of<br />
accuracy of theoretical results valid performing the thermodynamic<br />
limit but also because some qualitative features<br />
of the theory like spontaneous symmetry breaking<br />
appear only in this limit.<br />
Moreover, a generally accepted approximation, like<br />
the mean field, introduces new weakly interacting degrees<br />
of freedom and thus a “classical” (no entanglement)<br />
behaviour in terms of such degrees of freedom.<br />
It is then difficult to introduce approximations which<br />
preserve nonlocal properties, and thus most of the work<br />
done is based on exact results or numerical methods.<br />
Using the Bogoliubov approximation, we studied analitically<br />
the time evolution of entanglement in a system<br />
of interacting bosons (Bose-Hubbard model) considering<br />
an initial coherent state. In Figure 1 we show how the<br />
linear entropy, an entanglement monotone as far as globally<br />
pure states are considered, grows in time for different<br />
size systems.<br />
An alternative is to study either entanglement due to<br />
fluctuations with respect to mean field in the large size<br />
limit, or to modify the mean field approach to take into<br />
account the residual entanglement which arise from finite<br />
size effects. Recently the observation that some spin systems<br />
exhibit the mean field solution as the exact one for a<br />
particular value of a control parameter has led many people<br />
to study entanglement close to this particular point<br />
phase space in the large size limit.<br />
One of us (G.G.) proposed and studied new spin systems<br />
which exhibit a dimerized phase where entanglement<br />
disappears. It has been also showed how a finitesize<br />
analysis of such systems allows one to predict the<br />
appearence of a magnetic symmetry breaking once the<br />
thermodynamic limit is performed.<br />
To take into account size effects, we consider a generalization<br />
of mean-field superposition states originally<br />
introduced in the study of small superconductors and<br />
study the “residual”entanglement due to finite size effects.<br />
The extension to strongly interacting electron systems<br />
is in progress.<br />
References<br />
1. G. L. Giorgi et al., Phys. Rev. B 75, 064501 (2007).<br />
2. G. L. Giorgi et al., , Phys. Rev. A 78, 022305 (2008).<br />
3. F. de Pasquale, et al., Fortschr. Phys. 57, 1111 (2009).<br />
4. S. Paganelli, et al., Fortschr. Phys. 57, 1094 (2009).<br />
Authors<br />
F. de Pasquale, G. Giorgi, S. Paganelli<br />
1<br />
L inear entrop y<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0 5 10 15 20 25 30<br />
t<br />
Figure 1: Linear entropy of the one-mode density matrix<br />
as a function of time. The curves correspond to three<br />
different values of the size of the system: the blue line<br />
describes a Bose-Hubbard model with N = 2, the red<br />
line is for N = 8, while the black line corresponds to<br />
N = 20.<br />
<strong>Sapienza</strong> Università di Roma 97 Dipartimento di Fisica