@article{TEXTUAL,
      recid = {12114},
      author = {Hategan-Marandiuc, M.},
      title = {Entanglement entropy in lattices with non-Abelian gauge  groups},
      journal = {Physical Review D},
      address = {2024-05-06},
      number = {TEXTUAL},
      abstract = {Entanglement entropy, taken here to be geometric, requires  a geometrically separable Hilbert space. In lattice gauge  theories, it is not immediately clear if the physical  Hilbert space is geometrically separable. In a previous  paper we have shown that the physical Hilbert space in pure  gauge Abelian lattice theories exhibits some form of  geometric scaling with the lattice volume, which suggest  that the space is locally factorizable and, therefore,  geometrically separable. In this paper, we provide strong  evidence that indicates that this scaling is not present  when the group is non-Abelian. We do so by looking at the  scaling of the dimension of the physical Hilbert space of  theories with certain discrete groups. The lack of an  appropriate scaling implies that the physical Hilbert space  of such a theory does not admit a local factorization. We  then extend the reasoning, as sensibly possible, to SU(2)  and SU(N) to reach the same conclusion. Lastly, we show  that the addition of matter fields to non-Abelian lattice  gauge theories makes the resulting physical Hilbert space  locally factorizable.},
      url = {http://knowledge.uchicago.edu/record/12114},
}