# A contour for the entanglement entropies in harmonic lattices

## TL;DR

This paper develops a contour function for entanglement entropies in harmonic lattices, validating it through numerical analysis and comparison with conformal field theory predictions, especially in one-dimensional massless regimes.

## Contribution

It introduces a new contour function for entanglement entropy in harmonic lattices and compares it with theoretical predictions in specific regimes.

## Key findings

- Good agreement with conformal field theory in massless regimes
- Effective contour function for single and disjoint intervals
- Numerical validation across different boundary conditions

## Abstract

We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.