Heisenberg-Integrable Spin Systems

Autor(en): Steinigeweg, Robin 
Schmidt, Heinz-Juergen
Stichwörter: CLUSTERS; Completely integrable systems; FRUSTRATION; Heisenberg spin systems; Mathematics; Mathematics, Applied; Physics; Physics, Mathematical; STAR
Erscheinungsdatum: 2009
Herausgeber: SPRINGER
Journal: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY
Volumen: 12
Ausgabe: 1
Startseite: 19
Seitenende: 45
Zusammenfassung: 
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 explicitly calculated. The second class consists of spin systems where all non-zero coupling constants have the same strength (spin graphs) possessing N -aEuro parts per thousand 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 as vertex-induced sub-graphs. 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.
ISSN: 13850172
DOI: 10.1007/s11040-008-9050-y

Show full item record

Page view(s)

2
Last Week
0
Last month
0
checked on Mar 5, 2024

Google ScholarTM

Check

Altmetric