Entanglement hamiltonians in two-dimensional conformal field theory

TL;DR

This paper classifies cases in 2D conformal field theory where the entanglement Hamiltonian can be expressed as an integral over local energy-momentum tensors, including new time-dependent scenarios involving boundary effects.

Contribution

It extends the understanding of entanglement Hamiltonians in 2D CFTs to include time-dependent cases and highlights the role of boundary conditions and boundary entropies.

Findings

Entanglement Hamiltonian can be expressed as an integral over energy-momentum tensor in certain 2D CFT cases.

New examples include time-dependent scenarios like global and local quenches.

Boundary conditions at the entangling surface influence the entanglement spectrum and entropy.

Abstract

We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.