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

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.

35 pages, 15 figures

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• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Modular conjugations in 2D conformal field theory and holographic bit threads
• Entanglement Hamiltonians and the quasiparticle picture
• Modular Hamiltonian of the scalar field in the semi infinite line: dimensional reduction for spherically symmetric regions
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• On the mass dependence of the modular operator for a double cone
• Modular Hamiltonian for de Sitter diamonds
• Finite temperature negativity Hamiltonians of the massless Dirac fermion
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Entanglement Hamiltonian of a nonrelativistic Fermi gas
• Modular Hamiltonian for fermions of small mass
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain