Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice

TL;DR

This study uses advanced tensor network methods to reveal a novel gapped ground state and multiple magnetization plateaus in a frustrated quantum spin system on the ruby lattice, highlighting complex quantum phases.

Contribution

It demonstrates the existence of a gapped threefold-degenerate simplex crystal ground state and identifies multiple magnetization plateaus with supersolid phases in the spin-$1/2$ Heisenberg model on the ruby lattice.

Findings

Discovery of a gapped threefold-degenerate simplex crystal ground state.

Identification of magnetization plateaus at 0, 1/3, 1/2, and 2/3 of saturation.

Observation of supersolid phases breaking lattice rotational symmetry.

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.