Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

%B Phys. Rev. A 81 (2010) 062335 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3909 %1 800 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-27T07:32:21Z\\nNo. of bitstreams: 1\\n0912.0466v1.pdf: 336415 bytes, checksum: 7220d67cfb58f794aa50037140db23e6 (MD5) %R 10.1103/PhysRevA.81.062335 %0 Journal Article %J New J. Phys. 12 (2010) 075018 %D 2010 %T Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems %A Matteo Rizzi %A Simone Montangero %A Pietro Silvi %A Vittorio Giovannetti %A Rosario Fazio %XIn 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.

%B New J. Phys. 12 (2010) 075018 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4067 %1 335 %2 Physics %3 Condensed Matter Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-16T09:50:44Z\\nNo. of bitstreams: 1\\n10081611392421027.pdf: 1233170 bytes, checksum: 39da921aa8c098e7c8d6451b0ce08c15 (MD5) %R 10.1088/1367-2630/12/7/075018