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arXiv · 1504.05236

Chiral topological spin liquids with projected entangled pair states

Didier Poilblanc·J. Ignacio Cirac·Norbert Schuch
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Abstract

Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), we construct a family of chiral spin liquids on the square lattice which are generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from deformed local tensors with $d+i\, d$ symmetry. On a cylinder, we construct four topological sectors with even or odd number of spinons on the boundary and even or odd number of ($\mathbb{Z}_2$) fluxes penetrating the cylinder which, we argue, remain orthogonal in the limit of infinite perimeter. The analysis of the transfer matrix provides evidence of short-range (long-range) triplet (singlet) correlations as for the critical (non-chiral) RVB state. The Entanglement Spectrum exhibits chiral edge modes, which we confront to predictions of Conformal Field Theory, and the corresponding Entanglement Hamiltonian is shown to be long ranged.

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Didier Poilblanc, J. Ignacio Cirac, Norbert Schuch. 2015-07-08. Chiral topological spin liquids with projected entangled pair states. https://doi.org/10.1103/physrevb.91.224431

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