Low-lying numerical entanglement spectra (ES) can enable the identification of certain quantum states, based on “Li-Haldane state-counting”, as ground states of (2+1)-dimensional chiral topological phases. I will discuss how we can use CFT to quantitatively account for the splittings in such ES with global SU(2) symmetry, providing a diagnostic of the underlying topological theory with finer sensitivity than “state-counting”. The ES splittings arise from higher local conservation laws in the chiral CFT besides the energy, which can be viewed as a Generalized Gibbs Ensemble. We calculate conservation laws for chiral SU(2) Wess-Zumino-Witten CFTs at levels one and two, and for level two we find that some of the conservation laws are local integrals of operators of fractional dimension. I will show our analysis of numerical ES from some spin liquids with SU(2) symmetry, including two chiral Projected Entangled Pair States (PEPS), whose low-lying ES splittings can be well understood by our conservation laws. The states we consider, including the PEPS, appear chiral also under our more sensitive diagnostic.
ArXiv reference: https://arxiv.org/abs/2107.02545