Condensed Matter Seminar : Symmetry-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific symmetry sectors (commonly denoted as superselection sectors), this problem vanishes, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition – corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system. I will also discuss some thoughts and preliminary results regarding the meaning of superselection-resolved entanglement in LGT systems and its relation to their physics, and try to extract a minimal tensor network representation ansatz for LGT systems based on this relation.

[1] E. Zohar and M. Burrello, New J. Phys. (2016)