Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions

TL;DR

This paper investigates phase transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions, revealing continuous quantum phase transitions and symmetry cross-over behaviors in valence-bond solid states.

Contribution

It demonstrates continuous phase transitions in SU(2), SU(3), and SU(4) models with multi-spin interactions and analyzes the symmetry crossover near the transition.

Findings

Continuous quantum phase transitions with identical critical exponents.

Symmetry crossover from Z4 to U(1) near the phase transition.

Extension of transition analysis from SU(2) to higher N.

Abstract

We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.