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Evenbly, G; Vidal, G
Physical review letters, 2015-Nov-13, Volume: 115, Issue: 20Journal Article
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.
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