Operator content of real-space entanglement spectra at conformal critical points

TL;DR

This paper demonstrates that the low-lying entanglement spectrum of a one-dimensional quantum system at a conformal critical point reveals the operator content of the underlying boundary conformal field theory, enabling extraction of key CFT parameters.

Contribution

It establishes a direct link between the entanglement spectrum and the operator content of boundary CFTs, allowing for new insights into CFTs from wave function analysis.

Findings

Entanglement spectrum corresponds to boundary CFT energy spectrum.

Operator content of CFT can be inferred from entanglement spectrum.

Compactification radius of boson CFT can be deduced from entanglement data.

Abstract

We provide numerical evidence that the low-lying part of the entanglement spectrum of a real-space block (i.e. a single interval) of a one-dimensional quantum many body system at a conformal critical point corresponds to the energy spectrum of a boundary conformal field theory (CFT). This correspondence allows to uncover a subset of the operator content of a conformal field theory by inspection of the entanglement spectrum of a single wave function, thus providing important information on a CFT beyond its central charge. As a practical application we show that for many systems described by a compactified boson CFT, one can infer the compactification radius (governing e.g. the power law decay of correlation functions) of the theory in a simple way based on the entanglement spectrum.