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arXiv:2512.14173 · Physical review. B./Physical review. B

Simplex crystal ground state and magnetization plateaus in the spin- 1 2 Heisenberg model on the ruby lattice

Anonymous, Frédéric Mila

Published Jul 30, 2026• 0 citations
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Abstract

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 assumes a gapped threefold-degenerate simplex crystal ground state, with 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 inter-triangle 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 supersolid phases, all breaking the sixfold rotational symmetry of the lattice. Unlike the checkerboard lattice, these plateaus cannot be described by strongly localized magnons.

DOI
10.1103/h4xq-s7wp

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Theory of the 1/91/91/9 Magnetization Plateau of the Spin-1/21/21/2 Kagome Heisenberg Antiferromagnet
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We present a numerical study of the SU(NNN) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3N=3N=3) and the checkerboard lattice (for N=4N=4N=4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a twofold degeneracy, in which the NNN spins belonging to a simplex (i.e., a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models.