Entanglement spectra of (2+1)-dimensional topological spin liquid PEPS and chirality, with a focus on the SU(3)-symmetric case

The wavefunctions of (2+1)D chiral topological phases are often identified by studying low-lying entanglement spectra (ES) on long cylinders of finite circumference. For chiral topological states that possess global SU(3) symmetry, we can now understand the ES through the splitting of degeneracies in the finite-size ES, at a given momentum, solely from conformal field theory (CFT), a finer diagnostic than Li-Haldane "state-counting". We contrast such chiral ES with those of a non-chiral PEPS (Kurecic, Sterdyniak, and Schuch [PRB 99, 045116 (2019)]) with SU(3) symmetry. That PEPS has strong time-reversal and reflection symmetry breaking, but the full analysis of the sectors of the ES in prior work [arXiv:2207.03246] shows its non-chirality, in the sense of having zero chiral central charge. We can then identify a distinct indicator of chirality: the splittings of conjugate irreps. In the chiral ES, conjugate irreps are degenerate, because the operators (related to the cubic Casimir of SU(3)) that would split them are shown to be forbidden. In the non-chiral ES, conjugate splittings are non-negligible and can be calculated. Such a diagnostic simplifies identification of chirality in low-energy finite-size ES for SU(3)-symmetric topological states.