Ground States of the SU(N) Heisenberg Model

TL;DR

This paper investigates the ground states of the SU(N) Heisenberg model using quantum Monte Carlo simulations, revealing both qualitative agreement with theoretical predictions and unexpected degeneracy and order properties at various N values.

Contribution

It provides new numerical insights into the ground state properties of the SU(N) Heisenberg model across different representations and N values, highlighting phenomena not fully predicted by existing theories.

Findings

Ground states for N>=5 with fundamental representation show U(1) degeneracy.

No valence-bond-solid order observed for multi-column Young tableau representations.

Zero-temperature phase boundary aligns qualitatively with 1/N expansion predictions.

Abstract

The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N>=5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.