  We discuss Hamiltonian learning in quantum field theories as a protocol for
systematically extracting the operator content and coupling constants of
effective field theory Hamiltonians from experimental data. Learning the
Hamiltonian for varying spatial measurement resolutions gives access to field
theories at different energy scales, and allows to learn a flow of Hamiltonians
reminiscent of the renormalization group. Our method, which we demonstrate in
both theoretical studies and available data from a quantum gas experiment,
promises new ways of addressing the emergence of quantum field theories in
quantum simulation experiments.
