We prove an entanglement area law for a class of 1D quantum systems involving
infinite-dimensional local Hilbert spaces. This class of quantum systems
include bosonic models such as the Hubbard-Holstein model, and both U(1) and
SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new
results concerning the robustness of the ground state and spectral gap to the
truncation of Hilbert space, applied within the approximate ground state
projector (AGSP) framework from previous work. In establishing this area law,
we develop a system-size independent bound on the expectation value of local
observables for Hamiltonians without translation symmetry, which may be of
separate interest. Our result provides theoretical justification for using
tensor network methods to study the ground state properties of quantum systems
with infinite local degrees of freedom.
