Generalized Bell inequalities and frustrated spin systems
| dc.creator | Schmidt, Heinz-Jürgen | |
| dc.date | 2006-04-26 | |
| dc.date.accessioned | 2026-07-07T07:05:44Z | |
| dc.date.available | 2026-07-07T07:05:44Z | |
| dc.description | We find a close correspondence between generalized Bell inequalities of a special kind and certain frustrated spin systems. For example, the Clauser-Horn-Shimony-Holt inequality corresponds to the frustrated square with the signs +++- for the nearest neighbor interaction between the spins. Similarly, the Pearle-Braunstein-Cave inequality corresponds to a frustrated even ring with the corresponding signs +...+-. Upon this correspondence, the violation of such inequalities by the entangled singlet state in quantum mechanics is equivalent to the spin system possessing a classical coplanar ground state, the energy of which is lower than the Ising ground state's energy. We propose a scheme which generates new inequalities and give further examples, the frustrated hexagon with additional diagonal bonds and the frustrated hypercubes in n=3,4,5 dimensions. Surprisingly, the hypercube in n=4 dimensions yields an inequality which is not violated by the singlet state. We extend the correspondence to other entangled states and XXZ-models of spin systems. | |
| dc.description | 15 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0604591 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0604591 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109769 | |
| dc.subject | Materials Science | |
| dc.subject | Quantum Physics | |
| dc.title | Generalized Bell inequalities and frustrated spin systems | |
| dc.type | text |