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DY: Fachverband Dynamik und Statistische Physik

DY 7: Correlated Electrons: Nonequilibrium Quantum Many-Body Systems 1 (joint session TT/ DY)

DY 7.12: Talk

Monday, March 16, 2015, 12:45–13:00, H 0104

Holography of the toric code — •Johannes Oberreuter and Stefan Kehrein — Institut für Theoretische Physik, Georg-August-Universität Göttingen, Germany

Dynamics of quantum-many-body systems at weak coupling can be effectively described by quasi-particles. At strong coupling, the quasi-particle picture breaks down. Instead of resorting to numerics one can use a duality, which relates strongly coupled (conformal) field theories to classical, weakly coupled (Einstein) gravity in one dimension higher, the so-called gauge/gravity duality or AdS/CFT-correspondence. The correlation functions of the field theory can then in principle be computed from a calculation in classical gravity. The correspondence, however, in general only applies to conformal field theories and it is difficult to describe systems of interest in condensed matter theory. The observation of similarities in calculating the entanglement entropy in AdS/CFT and in MERA, a particular tensor network of a quantum state, has led to the conjecture that MERA might be a discrete version of the gauge-gravity duality. It is in principle possible to represent any quantum state in MERA. We investigate this idea in the toric code, where the representation is known exactly [1] and comment on the non-generic behaviour of this model including its dynamics.

[1] M. Aguado, G. Vidal, Phys. Rev. Lett. 100, 070404 (2008).