The reduced density matrix of a spatial subsystem can be written as the exponential of the entanglement (modular) Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. For some particular models, states and bipartitions, this operator is local, but in general it is expected to be non-local.
We discuss some entanglement Hamiltonians in two-dimensional conformal field theory and, in the case of free fermions, also how to obtain them from lattice calculations. The modular conjugation is closely related to the modular Hamiltonian. We discuss the geometric action of this operator in two-dimensional conformal field theory and its holographic gravitational counterpart in terms of geodesic bit threads.
