Toward Non-Abelian Chiral Spin Liquid PEPS Through Layered Construction

Can chiral topological states in (2+1)D be represented by Projected Entangled Pair States (PEPS)? For non-interacting fermionic PEPS, the answer is yes [1,2]. We consider instead the case of representation of chiral spin liquid (CSL) ground states by interacting PEPS (with finite bond dimension). Many PEPS are known that have properties of bona fide CSL ground states, both Abelian [3] and non-Abelian [4], but some uncertainties have remained. For instance, the half-integer spin sector of the entanglement spectrum can have two degenerate chiral branches. Meanwhile, in the non-Abelian [SU(2)-level-2] case, only two out of three topological sectors can be identified. Ref. [5] made substantial progress for the Abelian case in resolving many ambiguities (including the doubled branches) found to arise from the interplay of SU(2), point group, and translational symmetries in the PEPS. We now extend this understanding to non-Abelian CSL PEPS by building them up from Abelian chiral PEPS layers in a principled way. We analyze the resulting PEPS and are able to evaluate their ability to faithfully represent non-Abelian CSL ground states.

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[4] J.-Y. Chen, L. Vanderstraeten, S. Capponi, D. Poilblanc, Phys. Rev. B 98, 184409 (2018).

[5] A. Hackenbroich, A. Sterdyniak, N. Schuch, Phys. Rev. B 98, 085151 (2018).