Entanglement area law for 1D gauge theories and bosonic systems

In this talk I will introduce the proof of 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 and 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. Our result provides theoretical justification for using tensor networks to study the ground state properties of quantum systems with infinite local degrees of freedom.