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.
Highlights
Entanglement Hamiltonian of a sphere for the scalar fieldWe introduce the main expressions employed in this manuscript to study the entanglement Hamiltonian of a sphere in the d + 1 dimensional Minkowski spacetime for the scalar field in its ground state
When d = 1, specific conformal mappings have been constructed to obtain other entanglement Hamiltonians KA in the local form, i.e. written as an the integral over A of the energy density multiplied by the proper weight factor [15,16,17]
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
Summary
We introduce the main expressions employed in this manuscript to study the entanglement Hamiltonian of a sphere in the d + 1 dimensional Minkowski spacetime for the scalar field in its ground state.
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