A magnetic model with a possible Chern-Simons phase
| dc.creator | Freedman, Michael H. | |
| dc.date | 2001-10-09 | |
| dc.date | 2002-12-09 | |
| dc.date.accessioned | 2026-07-07T06:02:50Z | |
| dc.date.available | 2026-07-07T06:02:50Z | |
| dc.description | An elementary family of local Hamiltonians $H_{\c ,\ell}, \ell = 1,2,3, ldots$, is described for a $2-$dimensional quantum mechanical system of spin $={1/2}$ particles. On the torus, the ground state space $G_{\circ,\ell}$ is $(\log)$ extensively degenerate but should collapse under $ł$perturbation" to an anyonic system with a complete mathematical description: the quantum double of the $SO(3)-$Chern-Simons modular functor at $q= e^{2 πi/\ell +2}$ which we call $DE \ell$. The Hamiltonian $H_{\circ,\ell}$ defines a \underline{quantum} \underline{loop}\underline{gas}. We argue that for $\ell = 1$ and 2, $G_{\circ,\ell}$ is unstable and the collapse to $G_{ε, \ell} \cong DE\ell$ can occur truly by perturbation. For $\ell \geq 3$, $G_{\circ,\ell}$ is stable and in this case finding $G_{ε,\ell} \cong DE \ell$ must require either $ε> ε_\ell > 0$, help from finite system size, surface roughening (see section 3), or some other trick, hence the initial use of quotes $ł\quad$". A hypothetical phase diagram is included in the introduction. | |
| dc.description | Appendix by F. Goodman and H. Wenzl | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0110060 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0110060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89762 | |
| dc.subject | Quantum Physics | |
| dc.subject | Condensed Matter | |
| dc.subject | Geometric Topology | |
| dc.title | A magnetic model with a possible Chern-Simons phase | |
| dc.type | text |