First-order N\'eel-cVBS transition in a model square lattice $S=1$ antiferromagnet

TL;DR

This paper demonstrates that the quantum phase transition between Ne9el order and cVBS in an $S=1$ square lattice antiferromagnet is a first-order transition, contrasting with the continuous transition observed in the $S=1/2$ case.

Contribution

The study provides the first clear evidence of a first-order Ne9el-cVBS transition in an $S=1$ model, highlighting the impact of spin size on quantum critical behavior.

Findings

Evidence of a first-order transition through double-peaked histograms.

Observation of switching behavior indicative of phase coexistence.

Contrast with the $S=1/2$ case supporting the role of spin size in phase transitions.

Abstract

We study the N\'eel to four-fold columnar valence bond solid (cVBS) quantum phase transition in a sign free $S=1$ square lattice model. This is the same kind of transition that for $S=1/2$ has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square lattice $S=1/2$ N\'eel-VBS transition have found consistency with the DCP scenario with no direct evidence for first order behavior. In contrast to the $S=1/2$ case, in our quantum Monte Carlo simulations for the $S=1$ model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs for a first order transition demonstrating co-existence including double peaked histograms and switching behavior are observed. The sharp contrast from the $S=1/2$ case is remarkable, and is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two dimensional lattice models.