Tensor network renormalization yields the multi-scale entanglement renormalization ansatz

TL;DR

This paper introduces a method to construct MERA representations of ground states and thermal states of many-body Hamiltonians using tensor network renormalization, simplifying previous approaches and extending applicability.

Contribution

It presents a new way to build MERA states directly from tensor network renormalization, avoiding energy minimization and applying to both quantum and classical systems.

Findings

Efficient construction of MERA from TNR for ground states.

Extension of MERA to thermal Gibbs states.

Provides a renormalization group flow in wave-function space.

Abstract

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. 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.