Our research investigates gauge invariant models on lattices of two or higher dimensions, which are known to exhibit topologically-separated phases, making them promising for quantum error correction surface codes, and for numerical discretization of continuous gauge field theories. Specifically, we explore the properties of symmetry-resolved entanglement in these systems, which refers to the entanglement contributions between subsystems with different local charge sectors. Through this analysis, we aim to gain insight into the relationship between entanglement and symmetry. Notably, in scenarios where the charge is conserved within subsystems, the symmetry-resolved entanglement contributions are the only contributors to accessible entanglement.
Our results, based on a tensor network representation of gauge invariance, reveal that in a vast family of cases, the symmetry-resolved entanglement scales with the number of corners in the system, with a very weak dependence (if any) on system size. While corner-law contributions to entanglement have been observed previously, they have never been identified as the leading term. We analyze various cases and explore the relationship between our results and confinement in gauge-invariant models.