On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field

TL;DR

This paper investigates the continuum limit of the entanglement Hamiltonian for a sphere in a massless scalar field, using lattice discretization and numerical analysis to compare with conformal field theory predictions.

Contribution

It provides numerical evidence for the continuum limit of the entanglement Hamiltonian in a scalar field, confirming theoretical predictions in low angular momentum regimes.

Findings

Numerical results agree with conformal field theory predictions.

Dominant contributions are from on-site and nearest-neighbour terms at large mass.

Straight-line weight functions emerge for dominant terms.

Abstract

We study the continuum limit of the entanglement Hamiltonian of a sphere for the massless scalar field in its ground state by employing the lattice model defined through the discretisation of the radial direction. In two and three spatial dimensions and for small values of the total angular momentum, we find numerical results in agreement with the corresponding ones derived from the entanglement Hamiltonian predicted by conformal field theory. When the mass parameter in the lattice model is large enough, the dominant contributions come from the on-site and the nearest-neighbour terms, whose weight functions are straight lines.