Tensor network renormalization yields the multi-scale entanglement renormalization ansatz

Understand

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 \textit{tensor network renormalization} (TNR) [G.

• Evenbly and G.
• Vidal, arXiv:1412.0732] to the Euclidean time evolution operator $e^{-\beta H}$ for infinite $\beta$.
• This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature $\beta$, produces a MERA representation of a thermal Gibbs state.