  Entanglement is the fundamental difference between classical and quantum
systems and has become one of the guiding principles in the exploration of
high- and low-energy physics. The calculation of entanglement entropies in
interacting quantum field theories, however, remains challenging. Here, we
present the first method for the explicit computation of reduced density
matrices of interacting quantum field theories using truncated Hamiltonian
methods. The method is based on constructing an isomorphism between the Hilbert
space of the full system and the tensor product of Hilbert spaces of
sub-intervals. This naturally enables the computation of the von Neumann and
arbitrary R\'enyi entanglement entropies as well as mutual information,
logarithmic negativity and other measures of entanglement. Our method is
applicable to equilibrium states and non-equilibrium evolution in real time. It
is model independent and can be applied to any Hamiltonian truncation method
that uses a free basis expansion. We benchmark the method on the free
Klein-Gordon theory finding excellent agreement with the analytic results. We
further demonstrate its potential on the interacting sine-Gordon model,
studying the scaling of von Neumann entropy in ground states and real time
dynamics following quenches of the model.
