SU(N) Heisenberg model with multi-column representations

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase transitions in the SU(N) Heisenberg model with multi-column representations on a 2D lattice, revealing the nature of magnetic and valence-bond solid orders.

Contribution

It provides the first detailed numerical analysis of SU(N) Heisenberg models with multi-column representations, confirming theoretical predictions about phase transitions and orderings.

Findings

Valence-bond solid order appears at N=10 with two-column representations.

No magnetic or VBS order detected for N≥15 with three-column representations.

Results are consistent with large-N theoretical predictions.

Abstract

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