Entanglement and boundary critical phenomena

TL;DR

This paper explores boundary critical phenomena in quantum systems through entanglement measures, revealing how boundary effects influence entanglement and relate to boundary RG flows and the g-theorem.

Contribution

It introduces a boundary contribution to Renyi entropy, demonstrating entanglement loss along boundary RG flows and connecting it to majorization relations and the g-theorem.

Findings

Boundary entropy contributes to Renyi entropy.

Entanglement decreases along boundary RG flows.

Bulk and boundary contributions to entanglement differ in magnitude.

Abstract

We investigate boundary critical phenomena from a quantum information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S_alpha, which includes the von Neumann entropy (alpha=1) and the single-copy entanglement (alpha=infinity) as special cases. We identify the contribution from the boundary entropy to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g-theorem, can be regarded as a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.