Example of a first-order N\'eel to Valence-Bond-Solid transition in two-dimensions

TL;DR

This study investigates a quantum phase transition in a 2D spin model, revealing a strongly first-order Ne9el to VBS transition, contrasting with continuous transitions in similar models, highlighting the role of VBS symmetry.

Contribution

The paper demonstrates a first-order Ne9el to VBS transition in a 2D Heisenberg model with a specific multi-spin interaction, contrasting with previous models showing continuous transitions.

Findings

Transition is strongly first-order

No emergent U(1) symmetry due to staggered VBS pattern

Contrasts with continuous transitions in similar models

Abstract

We consider the $S=1/2$ Heisenberg model with nearest-neighbor interaction $J$ and an additional multi-spin interaction $Q_3$ on the square lattice. The $Q_3$ term consists of three bond-singlet projectors and is chosen to favor the formation of a valence-bond solid (VBS) where the valence bonds (singlet pairs) form a staggered pattern. The model exhibits a quantum phase transition from the N\'eel state to the VBS as a function of $Q_3/J$. We study the model using quantum Monte Carlo (stochastic series expansion) simulations. The N\'eel-VBS transition in this case is strongly first-order in nature, in contrast to similar previously studied models with continuous transitions into columnar VBS states. The qualitatively different transitions illustrate the important role of an emerging U(1) symmetry in the latter case, which is not possible in the present model due to the staggered VBS pattern (which does not allow local fluctuations necessary to rotate the local VBS order parameter).