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Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems

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Published 23 July 2010 Published under licence by IOP Publishing Ltd
, , Focus on Quantum Information and Many-Body Theory Citation M Rizzi et al 2010 New J. Phys. 12 075018 DOI 10.1088/1367-2630/12/7/075018

1367-2630/12/7/075018

Abstract

In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems. We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization strategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

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