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Lattice gauge theories (LGT) play a central role in modern physics, providinginsights into high-energy physics, condensed matter physics, and quantumcomputation. Due to the nontrivial structure of the Hilbert space of LGTsystems, entanglement in such systems is tricky to define. However, when onelimits themselves to superselection-resolved entanglement, that is,entanglement corresponding to specific gauge symmetry sectors (commonly denotedas superselection sectors), this problem disappears, and the entanglementbecomes well-defined. The study of superselection-resolved entanglement isinteresting in LGT for an additional reason: when the gauge symmetry isstrictly obeyed, superselection-resolved entanglement becomes the onlydistillable contribution to the entanglement. In our work, we study thebehavior of superselection-resolved entanglement in LGT systems. We employ atensor network construction for gauge-invariant systems as defined by Zohar andBurrello (2016) and find that, in a vast range of cases, the leading term insuperselection-resolved entanglement depends on the number of corners in thepartition, that is, corner-law entanglement. To our knowledge, this is thefirst case of such a corner-law being observed in any lattice system.

Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach