On entanglement hamiltonians of an interval in massless harmonic chains

TL;DR

This paper investigates the continuum limit of entanglement Hamiltonians in massless harmonic chains, comparing numerical results with conformal field theory predictions, and explores boundary effects on entanglement spectra.

Contribution

It provides a detailed analysis of entanglement Hamiltonians in massless harmonic chains, connecting numerical results with conformal field theory and boundary conditions.

Findings

Entanglement Hamiltonians match CFT predictions in the continuum limit.

Numerical spectra ratios align with boundary CFT operator content.

Boundary conditions influence the entanglement spectrum structure.

Abstract

We study the continuum limit of the entanglement hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning of a chain on the semi-infinite line with Dirichlet boundary conditions imposed at its origin. The entanglement hamiltonians of the interval predicted by Conformal Field Theory for the massless scalar field are obtained in the continuum limit. We also study the corresponding entanglement spectra and the numerical results for the ratios of the gaps are compatible with the operator content of the Boundary Conformal Field Theory of a massless scalar field with Neumann boundary conditions imposed along the boundaries introduced around the entangling points by the regularisation procedure.