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

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.

28 pages, 20 figures, 4 appendices. Improved with referee's comments

References in corpus (9)

• A class of quantum many-body states that can be efficiently simulated
• Surface/State Correspondence as a Generalized Holography
• Entanglement renormalization and topological order
• Entanglement renormalization, scale invariance, and quantum criticality
• Quantum MERA Channels
• Consistency Conditions for an AdS/MERA Correspondence
• Exact entanglement renormalization for string-net models
• From Path Integrals to Tensor Networks for AdS/CFT
• Constructing holographic spacetimes using entanglement renormalization

Cited by in corpus (1)

• Magic entanglement renormalization for quantum fields