The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders

Abstract

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 (iPEPS) for this, namely: (i) with simplex tensors and 9-site unit cell, and (ii) coarse-graining three spins in the Kagome lattice and mapping it to a square-lattice model with nearest-neighbor interactions, with 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 $m_z=\frac{1}{9},\frac{5}{9}$ and $\frac{7}{9}$ using a 9-site PEPS unit cell, the later set-up being able to accommodate $\sqrt{3}\times \sqrt{3}$ solid order. We also find that, at $m_z=\frac{1}{3}$, (lattice) nematic and $\sqrt{3}\times \sqrt{3}$ VBC-order states are degenerate within the accuracy of the 9-site simplex-method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1\times 2$ VBC-Solid orders. Within our accuracy, the 6-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even when the PEPS unit-cell is not commensurate with the expected ground state. 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 spin chain 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 networks.

7 pages, 8 figures, final version

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• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• Entanglement estimation in tensor network states via sampling
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach