SU(N) Heisenberg model with multicolumn representations

The $\mathrm{SU}\left(N\right)$ symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at $N=10$, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for $N\ge 15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

(by Tsuyoshi Okubo)

Reference:

T. Okubo, K. Harada, J. Lou and N. Kawashima: Phys. Rev. B 92, 134404 (2015).