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arXiv · 1804.06045

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

Adam Iaizzi·Kedar Damle·Anders W. Sandvik
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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.

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Adam Iaizzi, Kedar Damle, Anders W. Sandvik. 2018-04-17. Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model. https://doi.org/10.1103/physrevb.98.064405

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