Boundary quantum critical phenomena with entanglement renormalization

TL;DR

This paper extends entanglement renormalization techniques to boundary critical phenomena, enabling accurate modeling of boundary effects in quantum critical systems using a modified MERA approach.

Contribution

It introduces a boundary-augmented MERA framework to study boundary critical phenomena, connecting it to Wilson's RG and the Kondo problem.

Findings

Accurately approximates boundary critical ground states.

Extracts boundary scaling operators and dimensions.

Validates approach with quantum Ising model results.

Abstract

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.