  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.
