Entanglement renormalization for quantum fields with boundaries and defects

TL;DR

This paper extends the continuous Multiscale Entanglement Renormalization Ansatz (cMERA) framework to quantum field theories with boundaries and defects, demonstrating localized modifications of the entangler in a 1+1d free boson model.

Contribution

It introduces a method to incorporate boundaries and defects into cMERA, showing how the entangler adapts locally, inspired by the principle of minimal updates from lattice tensor networks.

Findings

Localized entangler modifications near boundaries and defects

Application demonstrated on 1+1d free boson cMERA

Framework consistent with conformal boundary conditions

Abstract

The continuous Multiscale Entanglement Renormalization Ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)] gives a variational wavefunctional for ground states of quantum field theoretic Hamiltonians. A cMERA is defined as the result of applying to a reference unentangled state a unitary evolution generated by a quasilocal operator, the entangler. This makes the extension of the formalism to the case where boundaries and defects are present nontrivial. Here we show how this generalization works, using the 1+1d free boson cMERA as a proof-of-principle example, and restricting ourselves to conformal boundaries and defects. In our prescription, the presence of a boundary or defect induces a modification of the entangler localized only to its vicinity, in analogy with the so-called principle of minimal updates for the lattice tensor network MERA.