2015/02/28 by Glen Evenbly, Guifre Vidal · 1 citation
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.115.200401
published as Phys. Rev. Lett. 115, 200401 (2015) · Revised version, with additional appendices. Main text: 5 pages, 4 figures, Appendices: 6 pages, 9 figures
arxiv created 2015/09/12 · arxiv updated 2015/11/18
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization (TNR) [G. Evenbly and G. Vidal, arXiv:1412.0732] 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 TNR with a renormalization group flow in the space of wave-functions and Hamiltonians (and not just in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.