This week my paper “Metamagnetism and zero-scale-factor universality in the two-dimensional J-Q model” came out in Physical Review B. This paper builds on my previous work studying the 1D J-Q model, focusing on the saturation transition at high magnetic field using quantum Monte Carlo and exact techniques.
Below a critical coupling value (Q/J)min, this saturation transition is continuous, and is an example of “zero-scale-factor” (ZSF) universality. In ZSF, the order parameter (in this case the magnetization) is described by a universal function of the bare coupling constants and no non-universal numbers (Sachdev, 1994). 2D is the upper critical dimension of ZSF, so we expect to see logarithmic violations of the scaling at low temperature. The form of these violations is predicted by Sachdev et al. This paper is the first numerical test of this form, and we find to our surprise that the logarithmic violations do not match the form proposed by Sachdev et al. The reasons for this are currently unclear and merit further investigation.
Above the coupling ratio (Q/J)min, the saturation transition take the form of a sudden magnetization jump an example of metamagnetism, a kind of first-order phase transition. This metamagnetic transition is broadly similar to the one discovered in our previous work on the 1D J-Q model (Iaizzi, 2017). It is caused by the onset of bound states of magnons (spin flips against a polarized background). Using an exact method, we extract the value of (Q/J)min.
This paper is available directly from PRB (paywall); it can also be found on arxiv, or as a free PDF here.
Thanks to my coauthors Kedar Damle and Anders Sandvik.
I just submitted a new manuscript to PRB and posted it on arXiv (arXiv:1804.06045). This paper is a collaboration with Anders Sandvik and Kedar Damle. This is paper builds on our previous work on the field-driven saturation transition in the 1D J-Q model to study the saturation transition in 2D.
Fig 4. Magnetization density as a function of field for various values of s=Q with J+Q=1.
Metamagnetism: Using QMC, we find magnetization jumps to the saturated state (metamagnetism) above a critical coupling ratio (Q/J)min. We then use an exact method based on a high magnetization expansion to determine (Q/J)min. Above (Q/J)min the saturation transition is discontinuous (featuring a magnetization jump) and below (Q/J)min the transition is continuous.
Zero-scale-factor universality: When the saturation transition is continuous it is governed by zero-scale-factor universality. First proposed by Sachdev, Senthil and Shankar in 1994, zero-scale-factor universality is characterized by response functions that depend only on the bare parameters and no non-universal numbers. Remarkably, there had be no previous numerical or experimental verification of the scaling forms predicted in the 1994 Sachdev paper. Our QMC results confirm that the leading order scaling forms work and find logarithmic divergences at low temperature. These divergences are to be expected, since two spatial dimensions is the upper critical dimension of the zero-scale-factor universality, and the Sachdev paper even proposes a form for this divergence. When comparing to our QMC results, we find that the Sachdev form for the logarithmic divergences does not appear to be correct.
If you would like to know more all the details are on arxiv.