Classes of integrable spin systems
Steinigeweg, Robin ; Schmidt, Heinz-Jürgen
arXiv, 0504009 / Harvested from arXiv
Text on arXiv
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two uniformly coupled or disjoint subsystems with property $P$. For these systems the time evolution can be explicitely calculated. The second class consists of spin systems where all non-zero coupling constants have the same strength (spin graphs) possessing $N-1$ independent, commuting constants of motion of Heisenberg type. These systems are shown to have the above property $P$ and can be characterized as spin graphs not containing chains of length four. We completely enumerate and characterize all spin graphs up to N=5 spins. Applications to the construction of symplectic numerical integrators for non-integrable spin systems are briefly discussed.
Publié le : 2005-04-04
Classification:  Mathematical Physics,  Condensed Matter - Other Condensed Matter,  70H06, 37J35, 81Q05, 94C15, 82D40 
@article{0504009,
     author = {Steinigeweg, Robin and Schmidt, Heinz-J\"urgen},
     title = {Classes of integrable spin systems},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504009}
}

Steinigeweg, Robin; Schmidt, Heinz-Jürgen. Classes of integrable spin systems. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504009/