Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model

TL;DR

This study investigates the saturation transition in the 2D $J$-$Q$ model, confirming zero-scale-factor universality with unexpected logarithmic corrections and revealing a first-order transition with metamagnetism at higher couplings.

Contribution

It provides the first detailed analysis of the saturation transition in the 2D $J$-$Q$ model, including an exact solution for the critical coupling and insights into the transition's nature.

Findings

Conforms to zero-scale-factor universality with logarithmic corrections

Transition becomes first order with magnetization jumps at higher $Q/J$

Exact solution for critical coupling ratio $(Q/J)_{min}$

Abstract

Using a combination of quantum Monte Carlo and exact methods, we study the field-driven saturation transition of the two-dimensional $J$-$Q$ model, in which the antiferromagnetic Heisenberg exchange $(J)$ coupling competes with an additional four-spin interaction $(Q)$ that favors valence-bond solid order. For small values of $Q$, the saturation transition is continuous, and is expected to be governed by zero-scale-factor universality at its upper critical dimension, with a specific form of logarithmic corrections to scaling (first proposed by Sachdev \textit{et al.} [Phys. Rev. B \textbf{50}, 258 (1994)]). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev \textit{et al.} We also show that the saturation transition becomes first order above a critical coupling ratio $(Q/J)_{\rm min}$ and is accompanied by magnetization jumps---metamagnetism. We obtain an exact solution for $(Q/J)_{\rm min}$ using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations.