Unambiguous diagnostic of chirality in the entanglement spectrum of (2+1)d topological spin liquids: Demonstration in a SU(4) PEPS

We address the key question of representation of chiral topological quantum states in (2+1)d by Projected Entangled Pair States (PEPS). A noted result (due to Wahl, Tu, Schuch, and Cirac [arXiv:1308.0316] and Dubail and Read [arXiv:1307.7726]) says this is possible for non-interacting fermions, but the answer is as yet unknown for interacting systems. Characteristic counting of degeneracies of low-lying states in the entanglement spectrum (ES) at fixed transverse momentum of bipartitioned long cylinders ("Li-Haldane counting") provides often-used supporting evidence for chirality. However, non-chiral states (with zero chiral central charge), yet strongly breaking time-reversal and reflection symmetries (i.e., "apparently" chiral states), are known [arXiv:2207.03246], whose low-lying ES exhibits the same Li-Haldane counting as a chiral state (with non-zero chiral charge) in certain topological sectors. We recently identified [arXiv:2305.13240] a hallmark of chirality of a wave function in the ES in SU(3) chiral spin liquids, which is a finer diagnostic than Li-Haldane counting: The exact degeneracies of entanglement-energy levels in the ES corresponding to paired conjugate representations, which are split in non-chiral states. Here we identify an analogous hallmark of chirality of wave functions of SU(4) spin liquids and demonstrate its use in a SU(4) PEPS.