Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices

TL;DR

This paper numerically investigates SU(N) Heisenberg models on kagome and checkerboard lattices, revealing that their ground states are simplex solids with specific degeneracies, generalizing valence bond states.

Contribution

It demonstrates that the ground states of these SU(N) models are simplex solids, extending the understanding of valence bond states to more complex lattices and higher symmetries.

Findings

Ground states are simplex solids with two-fold degeneracy.

Spins in a simplex form a singlet, generalizing valence bond states.

Results obtained using iPEPS and exact diagonalization.

Abstract

We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3) and the checkerboard lattice (for N=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 (iPEPS) and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a two-fold ground state degeneracy, in which the N 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.