Beyond Li-Haldane Counting: A Close Look at Chiral Topological Order in the Entanglement Spectra of (2+1)-Dimensional Spin Liquid Ground States, with a Focus on PEPS

by Dr Mark Arildsen (SISSA, Trieste)

Friday 15 Dec 2023, 11:00 → 12:00 Europe/Zurich

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Whether chiral topological quantum states in (2+1)d can be represented by Projected Entangled Pair States (PEPS) is a fundamental question. A noted result (due to Wahl, Tu, Schuch, and Cirac, and Dubail and Read) says that 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. In this talk, I will discuss our work on understanding the ES beyond Li-Haldane counting in the case of ground states of SU(2) and SU(3) chiral spin liquids. We examine the splittings of degeneracies in entanglement energy, which are determined by the generalized Gibbs ensemble (GGE) of local conserved quantities from CFT that respect the symmetries of the system. This information serves as a finer diagnostic (than the countings alone) of chiral topological behavior. It turns out that non-chiral states (with zero chiral central charge), yet strongly breaking time-reversal and reflection symmetries (i.e., "apparently" chiral states), are known, whose low-lying ES exhibits the same Li-Haldane counting as a chiral state (with non-zero chiral charge) in certain topological sectors. By studying the splittings of the ES in an Abelian SU(3) spin liquid PEPS, we recently identified a hallmark of chirality of a wave function: The exact degeneracies of entanglement-energy levels in the ES corresponding to paired conjugate representations, which are split in non-chiral states.