Speaker
Description
Entanglement in lattice gauge theories (LGTs) is a topic of significant interest, but its definition and measurement are complicated by the fundamental structure of the Hilbert space. The gauge-invariance condition makes the total Hilbert space non-factorizable into local subsystems, thus precluding the direct application of standard entanglement measures like the von Neumann or Rényi entropies. By reorganizing the gauge degrees of freedom (DoF) in a novel way, we introduce a consistent and physically meaningful method to bipartition the system. This approach ensures that each subsystem remains gauge-invariant, allowing for a product Hilbert space structure. We demonstrate that the entanglement extracted from this bipartition, which we term "underlying plaquette entanglement" (UPE), provides a robust measure of entanglement that respects the unique properties of LGTs. Our generalization of the plaquette formalism, originally defined for $Z_2$ pure gauge theories, extends to different gauge groups and includes matter fields. This equivalent, local model without redundant degrees of freedom offers a new avenue for theoretical studies and tensor network simulations of lattice and field gauge theories.
