We investigate the spin-$1/2$ Heisenberg antiferromagnet on the ruby lattice with uniform first- and second-neighbor interactions, which forms a two-dimensional network of corner-sharing tetrahedra. Using infinite projected entangled pair states (iPEPS), we study the ground state of the system to find that it is consistent with a gapped, threefold-degenerate simplex crystal phase, characterized by strong singlets formed on pairs of neighboring triangles. We argue that the formation of the simplex singlet ground state at the isotropic point relates to the weak intertriangle coupling limit, where an effective spin-chirality Hamiltonian on the honeycomb lattice exhibits an extensively degenerate ground state manifold of singlet coverings at the mean-field level. Under an applied Zeeman field, the iPEPS simulations uncover magnetization plateaus at $m/m_s=0,1/3,1/2,$ and $2/3$, separated by intermediate candidate supersolid phases, with partial reduction of the sixfold rotational symmetry of the lattice. Unlike the checkerboard lattice, these plateaus cannot be described by strongly localized magnons.

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• Frustrated magnetism
• Projected entangled pair states
• Spontaneous symmetry breaking
• 2-dimensional systems
• Antiferromagnets
• Magnetic systems