We study numerically the spin-1/2 XXZ model in a field on an infinite kagome lattice. We use different algorithms based on infinite projected entangled pair states (iPEPSs) for this, namely, (i) an approach with simplex tensors and a 9-site unit cell, and (ii) an approach based on coarse-graining three spins in the kagome lattice and mapping it to a square-lattice model with local and nearest-neighbor interactions, with the usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at ${m}_{z}=\frac{1}{3}$ using 6-, 9-, and 12-site PEPS unit cells, and at ${m}_{z}=\frac{1}{9},\phantom{\rule{0.28em}{0ex}}\frac{5}{9}$ , and $\frac{7}{9}$ using a 9-site PEPS unit cell, the latter setup being able to accommodate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ solid order. We also find that, at ${m}_{z}=\frac{1}{3}$ , (lattice) nematic and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1\ifmmode\times\else\texttimes\fi{}2$ VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.We study numerically the spin-1/2 XXZ model in a field on an infinite kagome lattice. We use different algorithms based on infinite projected entangled pair states (iPEPSs) for this, namely, (i) an approach with simplex tensors and a 9-site unit cell, and (ii) an approach based on coarse-graining three spins in the kagome lattice and mapping it to a square-lattice model with local and nearest-neighbor interactions, with the usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at ${m}_{z}=\frac{1}{3}$ using 6-, 9-, and 12-site PEPS unit cells, and at ${m}_{z}=\frac{1}{9},\phantom{\rule{0.28em}{0ex}}\frac{5}{9}$, and $\frac{7}{9}$ using a 9-site PEPS unit cell, the latter setup being able to accommodate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ solid order. We also find that, at ${m}_{z}=\frac{1}{3}$, (lattice) nematic and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1\ifmmode\times\else\texttimes\fi{}2$ VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.

arXiv:1608.00437Physical review. B./Physical review. BDec 20, 201625 citations

Phases of the frustrated XY model on the honeycomb lattice

Juan Carrasquilla, Andrea Di Ciolo, Federico Becca +2 more

Bulletin of the American Physical SocietyMar 5, 20140 citations

{m}_{z}=\frac{1}{3}

using 6-, 9-, and 12-site PEPS unit cells, and at

{m}_{z}=\frac{1}{9},\phantom{\rule{0.28em}{0ex}}\frac{5}{9}

, and

\frac{7}{9}

using a 9-site PEPS unit cell, the latter setup being able to accommodate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ solid order. We also find that, at

{m}_{z}=\frac{1}{3}

, (lattice) nematic and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1\ifmmode\times\else\texttimes\fi{}2$ VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.