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.

PB - American Physical Society UR - http://hdl.handle.net/1963/3909 U1 - 800 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems JF - New J. Phys. 12 (2010) 075018 Y1 - 2010 A1 - Matteo Rizzi A1 - Simone Montangero A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Rosario Fazio AB -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.

PB - IOP Publishing UR - http://hdl.handle.net/1963/4067 U1 - 335 U2 - Physics U3 - Condensed Matter Theory ER -