Entanglement spectrum in one-dimensional systems

TL;DR

This paper derives a universal formula for the entanglement spectrum in 1D systems using conformal field theory, verifies it with the XX chain, and discusses how the entanglement gap diminishes as the block size grows.

Contribution

It provides a universal scaling function for the entanglement spectrum in 1D systems based on conformal field theory, validated by exact XX chain results.

Findings

Universal entanglement spectrum distribution derived

Validation with exact XX chain results

Entanglement gap closes with increasing block size

Abstract

We derive the distribution of eigenvalues of the reduced density matrix of a block of length l in a one-dimensional system in the scaling regime. The resulting "entanglement spectrum" is described by a universal scaling function depending only on the central charge of the underlying conformal field theory. This prediction is checked against exact results for the XX chain. We also show how the entanglement gap closes when l is large.