Physical realization of the four color problem in quantum systems
| dc.creator | Yamanaka, Masanori | |
| dc.creator | Tanaka, Akinori | |
| dc.date | 2005-10-07 | |
| dc.date.accessioned | 2026-07-07T06:44:10Z | |
| dc.date.available | 2026-07-07T06:44:10Z | |
| dc.description | A multi-component electron model on a lattice is constructed whose ground state exhibits a spontaneous ordering which follows the rule of map-coloring used in the solution of the four color problem. The number of components is determined by the Euler characteristics of a certain surface into which the lattice is embedded. Combining the concept of chromatic polynomials with the Heawood-Ringel-Youngs theorem, we derive an index theorem relating the degeneracy of the ground state with a hidden topology of the lattice. The system exhibits coloring transition and hidden-topological structure transition. The coloring phase exhibits a topological order. | |
| dc.description | 5 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0510161 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0510161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102685 | |
| dc.subject | Strongly Correlated Electrons | |
| dc.subject | Other Condensed Matter | |
| dc.title | Physical realization of the four color problem in quantum systems | |
| dc.type | text |