Entanglement renormalization and wavelets

TL;DR

This paper reveals a precise link between wavelet transforms and entanglement renormalization, using Daubechies wavelets to construct analytic MERA states for critical quantum systems, advancing understanding of quantum many-body states.

Contribution

It establishes a direct connection between wavelet transforms and MERA, providing the first analytic construction of MERA for critical systems.

Findings

Wavelet-based states approximate the ground state of the critical Ising model.

These states correspond to instances of the MERA ansatz.

The work provides the first known analytic MERA for critical systems.

Abstract

We establish a precise connection between discrete wavelet transforms (WTs) and entanglement renormalization (ER), a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multi-scale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.