Regensburg 2013 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster II

DY 33.49: Poster

Donnerstag, 14. März 2013, 17:00–19:00, Poster C

MERA-networks as holographic duals for the random Heisenberg spin-chain — •Johannes Oberreuter and Stefan Kehrein — Georg-August-Universität Göttingen, Germany

The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. A strongly coupled field theory is dual to weakly coupled, classical gravity. This allows to do a calculation of correlation functions for a strongly coupled theory in the weakly coupled counterpart perturbatively. Thereby, the extra (radial) dimension represents the scale of the RG transformation in the field theory. Real space renormalization procedures like the multi-scale-renormalization-ansatz (MERA) can be used to determine the ground state of the field theory. It has been conjectured, that the tensor networks which arise during this procedure are a discretized version of Anti-de Sitter space, which is the background of the gravity theory, for which the duality is established best (AdS/CFT-correspondence). It was so far impossible to construct such a network explicitely. We consider the dual network of a random Heisenberg spin-chain, for which real-space renormalization can be performed analytically. After establishing the form of the network at finite temperature, we examine quenches in the spin-chain to study the relation between the MERA-network and the Heisenberg chain far from equilibrium.