# Entanglement and correlations in the continuous multi-scale entanglement renormalization ansatz

## TL;DR

This paper analyzes the entanglement structure of the continuous multi-scale entanglement renormalization ansatz (cMERA) for quantum field theories, demonstrating that it avoids UV divergences in correlations and entanglement entropy in free models.

## Contribution

It provides explicit calculations showing that Gaussian cMERA states for free QFTs have no UV divergences in correlations and entanglement entropy, unlike exact ground states.

## Key findings

- cMERA states lack UV divergences in two-point functions
- cMERA avoids UV divergences in entanglement entropy
- Results are shown for free bosonic and fermionic QFTs in 1+1 and 2+1 dimensions

## Abstract

We investigate the entanglement structure of the continuous multi-scale entanglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett., 110, 100402 (2013)] for ground states of quantum field theories (QFTs). The cMERA, proposed as an extension to QFTs of the lattice MERA, is defined directly in the continuum but is nevertheless naturally equipped with a short-distance scale $1/\Lambda$ that acts as a UV regulator for quantum fluctuations. We consider the simplified setting of Gaussian cMERA for free QFTs, where explicit calculations can be performed. For relativistic free massless bosonic and fermionic QFTs in both 1+1 and 2+1 spacetime dimensions, we show that the cMERA state indeed displays no UV divergences in two-point correlation functions or entanglement entropy, in sharp contrast with the exact ground states.