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