title: Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.
abstract: We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
authors.affiliation: Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA.
authors.forename: G
authors.initials: G
authors.lastname: Evenbly
authors.affiliation: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: G
authors.initials: G
authors.lastname: Vidal