Saturation Transition in the 2D J-Q Model

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 et al., Phys Rev B 50:258, 1994). Our results conform to this expectation, but the logarithmic corrections to scaling do not match the form predicted by Sachdev et al.; we discuss an alternative scaling form based on the 4D Ising universality class. We also show that the saturation transition becomes first order above a critical coupling ratio (Q∕J)_min and is accompanied by magnetization jumps—metamagnetism. We obtain an exact solution for (Q∕J)_min using a high magnetization expansion, and confirm the existence of the magnetization jumps beyond this value of coupling using quantum Monte Carlo simulations. A version of this chapter without the discussion on 4D Ising universality was published in Phys Rev B 98:064405, 2018.

A version of this chapter without the discussion on 4D Ising universality titled “Metamagnetism and zero-scale-factor universality in the two-dimensional J-Q model” and coauthored with Anders W. Sandvik and Kedar Damle has been published in https://doi.org/Physical Review B 98 064405 (2018) [1]. Reprinted with permission.