Investigation of the chiral antiferromagnetic Heisenberg model using PEPS

TL;DR

This paper constructs and optimizes chiral PEPS for a frustrated antiferromagnetic Heisenberg model, revealing chiral edge modes and long-range correlations, advancing understanding of chiral spin liquids.

Contribution

It introduces low bond dimension chiral PEPS that outperform the KL ansatz and analyzes their edge modes and correlation properties.

Findings

Optimal D=3 PEPS exhibits SU(2)_1 chiral edge modes.

PEPS spin liquids show power-law dimer correlations.

Long-range tails observed in spin-spin correlations.

Abstract

A simple spin-$1/2$ frustrated antiferromagnetic Heisenberg model (AFHM) on the square lattice - including chiral plaquette cyclic terms - was argued [Anne E.B. Nielsen, German Sierra and J. Ignacio Cirac, Nature Communications $\bf 4$, 2864 (2013)] to host a bosonic Kalmeyer-Laughlin (KL) fractional quantum Hall ground state [V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. $\bf 59$, 2095 (1987)]. Here, we construct generic families of chiral projected entangled pair states (chiral PEPS) with low bond dimension ($D=3,4,5$) which, upon optimization, provide better variational energies than the KL ansatz. The optimal $D=3$ PEPS exhibits chiral edge modes described by the Wess-Zumino-Witten $SU(2)_1$ model, as expected for the KL spin liquid. However, we find evidence that, in contrast to the KL state, the PEPS spin liquids have power-law dimer-dimer correlations and exhibit a gossamer long-range tail in the spin-spin correlations. We conjecture that these features are genuine to local chiral AFHM on bipartite lattices.