Hamburg 2009 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 39: Quanteninformation: Konzepte V
Q 39.5: Vortrag
Mittwoch, 4. März 2009, 17:30–17:45, VMP 6 HS-D
Unifying all classical spin models in a Lattice Gauge Theory — •Gemma De las Cuevas1,2, Wolfgang Duer1,2, Hans J. Briegel1,2, and Miguel Angel Martin-Delgado3 — 1Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria — 2Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Innsbruck, Austria — 3Departamento de Física Teórica I, Universidad Complutense, 28040. Madrid, Spain
We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d≥ 4, and we show that the computation of the partition function of the 4D Z2 LGT is a computationally hard (#P-hard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z2 LGT. All results are proven using quantum information techniques.