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Résumé |
Integrable systems like the spin-1/2 Heisenberg chain provide the rare
opportunity of calculating exact results like energies and thermodynamics for
finite size and in the thermodynamic limit. We know many integrable systems
for many decades, but actual calculations of physical properties have only
rather recently been done if at all.
A notorious problem is posed by the computation of correlation functions. For
the infinite volume system, even static correlators present a major
challenge. Currently, we know how to calculate short range correlators for the
spin-1/2 Heisenberg chain at arbitrary temperature and magnetic field, where
the first results for zero temperature and zero magnetic field have been
obtained about 20 years ago. A central result of Jimbo, Miwa, Smirnov and
others is the factorization of general static correlators into sums over
products of nearest-neighbour correlators similar to the Wick theorem for
ideal quantum systems however with much more complicated structure factors.
There are applications in the field of non-equilibrium systems such as
interaction quenches. I will talk about applications of the computational
methods for the study of the stationary state approached through the
equilibration process. A major subject of my talk will be the generalization
of the study of correlation functions in direction of higher spin-S chains
with su(2) symmetry and into the direction of higher rank symmetry like su(3). |
