Linear independence of localized magnon states
Autor(en): | Schmidt, Heinz-Juergen Richter, Johannes Moessner, Roderich |
Stichwörter: | BEHAVIOR; DISORDER; EXCITATIONS; FIELD; FRUSTRATED MAGNETS; GROUND-STATES; HEISENBERG-ANTIFERROMAGNET; KAGOME LATTICE; LADDERS; Physics; Physics, Mathematical; Physics, Multidisciplinary; SPIN CHAIN | Erscheinungsdatum: | 2006 | Herausgeber: | IOP PUBLISHING LTD | Enthalten in: | JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | Band: | 39 | Ausgabe: | 34 | Startseite: | 10673 | Seitenende: | 10690 | Zusammenfassung: | At the magnetic saturation field, certain frustrated lattices have a class of states known as `localized multi-magnon states' as exact ground states. The number of these states scales exponentially with the number N of spins and hence they have a finite entropy also in the thermodynamic limit N -> infinity provided they are sufficiently linearly independent. In this paper, we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices, including what we call the orthogonal type and the isolated type, as well as the kagome, the checkerboard and the star lattice, we have proven linear independence of all localized multi-magnon states. On the other hand, the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence. |
ISSN: | 03054470 | DOI: | 10.1088/0305-4470/39/34/006 |
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geprüft am 06.06.2024