SU(2)${}_1$ chiral edge modes of a critical spin liquid

Abstract

Protected chiral edge modes are a well-known signature of topologically ordered phases like the Fractional Quantum Hall States. Recently, using the framework of projected entangled pair states (PEPS) on the square lattice, we constructed a family of chiral Resonating Valence Bond states with ${\mathbb{Z}}_2$ gauge symmetry. Here we revisit and analyze in full details the properties of the edge modes as given by their Entanglement Spectra on a cylinder. Surprisingly, we show that the latter can be well described by a chiral SU(2)${}_1$ Conformal Field Theory (CFT), as for the $\nu =1/2$ (bosonic) gapped Laughlin state, although our numerical data suggest a critical bulk compatible with an emergent $U(1)$ gauge symmetry. We propose that our family of PEPS may physically describe a boundary between a chiral topological phase and a trivial phase.

9 pages, 10 figures. v2: minor changes in introduction, refs added

References in corpus (9)

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• Resonating valence bond states in the PEPS formalism
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
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• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice

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