01188nas a2200157   4500008004300000245010800043210006900151260001900220520065100239100001800890700002300908700001800931700002600949700001900975856003600994       2010                        en_Ud  00aHomogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems0 aHomogeneous multiscale entanglement renormalization ansatz tenso  bIOP Publishing3 a<p>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\\nstrategies. 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.</p>1 aRizzi, Matteo1 aMontangero, Simone1 aSilvi, Pietro1 aGiovannetti, Vittorio1 aFazio, Rosario  uhttp://hdl.handle.net/1963/4067