Category Archives: paper

My dissertation is now available online from Springer!

The cover of my dissertation as published by Springer

Earlier this year David Campbell nominated my dissertation for a Springer Thesis Award. I’m proud to say that my dissertation won and it is now available from Springer. My dissertation covers almost all of the research I did during my PhD, focusing on magnetic field effects on quantum antiferromagnets, specifically metamagnetism and deconfined quantum criticality. I’m especially proud of my introduction (Ch. 1), which I tried to make accessible to a relatively broad audience, and my methods chapter (Ch. 5), a detailed pedagogical guide to the numerical methods I used in my work.

In Chapter 1 I describe the historical and scientific context for both the study I have undertaken and the methods I have used to do it. In doing so, I tell the story of Dr. Arianna Wright Rosenbluth, the woman physicist who wrote the first-ever modern Monte Carlo algorithm in 1953. To my knowledge this is the most complete account of her life ever published.

Chapter 2 is a lightly edited version of my 2017 Phys. Rev. B paper on metamagnetism and zero-scale-factor universality in the 1D J-Q model. In Chapter 3 I discuss these same features in the 2D J-Q model. Most of Chapter 3 has been published in my 2018 Phys. Rev. B paper, but the Springer version includes an additional analysis where we look at an alternative form of the logarithmic corrections to the zero-scale-factor universality based on the 4D Ising universality.

In Chapter 4 I study the deconfined quantum critical point separating the Néel and VBS phases in the 2D J-Q model. Using a field, I force a nonzero density of magnetic excitations and show that their thermodynamic behavior is consistent with deconfined spinons (the fractional excitations predicted by deconfined quantum criticality). I also discuss a field-induced BKT transition and non-monotonic temperature dependence of magnetization, a little-known feature of this type of transition.

Finally, in Chapter 5  I provide a detailed pedagogical description of my methods focusing on stochastic series expansion quantum Monte Carlo and extensions thereof. Little in this chapter is my invention, but many of the details of these techniques have not been described in detail anywhere else in the literature (another resource is Sandvik’s excellent review article).

If you’re interested in using my dissertation, please let me know and I can send you a PDF!


My dissertation won a Springer Thesis Award

I’m thrilled to announce that my dissertation “Magnetic field effects in low-dimensional quantum magnets” has been selected for a Springer Thesis Award and will be published by Springer. The manuscript is still in production (currently scheduled for publication November 27), but the listing is live on Springer’s website now.* Thanks again to my PhD advisor, Anders Sandvik and my committee, Rob Carey, Shyam Erramilli, Claudio Chamon and David Campbell as well as my department chair Andrei Ruckenstein. A special thanks to David for nominating my dissertation for this award.

*Let me know if you want to read it.

What is condensed matter physics?

Below is a lightly-edited excerpt from Ch. 1 of my dissertation in which I describe my field in the broadest possible terms. My dissertation is currently in production for publication in the “Springer Theses” series.


This dissertation is in the field of condensed matter physics, which in the most informal sense possible, could be described as ‘the study of stuff that is not especially hot nor moving especially fast’  [1]. A more formal (but no less vague) definition is ‘the study of the behavior of large collections of interacting particles’ [2]. The haziness of this definition is appropriate since condensed matter is a very broad field encompassing the study of almost all everyday matter including liquids, solids and gels as well as exotic matter like superconductors. Condensed matter physics is a tool for answering questions like: Why are some materials liquids? Why are others magnetic? What sorts of materials make good conductors of electricity? Why are ceramics brittle? Our understanding of condensed matter physics underlies much of modern technology; some prominent examples include ultra-precise atomic clocks, transistors [3], lasers, and both the superconducting magnets and the superconducting magnetometers used for magnetic resonance imaging (MRI). Condensed matter physics overlaps with the fields of magnetism, optics, materials science and solid state physics.

Condensed matter physics is concerned with the behavior of large collections of particles. These particles are easy to define: they will sometimes be atoms or molecules and occasionally electrons and nuclei; condensed matter is almost never concerned with any behavior at higher energy scales (i.e. no need to worry about quarks). The key word in the definition is large. Atoms are very small, so any macroscopic amount of matter has a huge number of them, somewhere around Avogadro’s number: 1023. Large ensembles of particles display emergent phenomena that are not obvious consequences of underlying laws that govern the behavior of their microscopic components. In the words of P.W. Anderson:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. …hierarchy does not imply that science X is “just applied Y.” At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry. [4]

Emergent phenomena are not merely difficult to predict from the underlying microscopic laws, but they are effectively unrelated. At the most extreme scale, no one would argue that consciousness is somehow a property of standard model particles, or that democracy is a state that could ever be described in terms of quantum field theory. Here I will focus on two such emergent phenomena: phase transitions, where symmetries of the underlying laws are spontaneously violated and behavior is independent of microscopic details, and quasiparticles, an almost infinite variety of excitations of many-body states of matter that bear no resemblance to the ‘real’ particles that make up the matter itself [5].

The most interesting problems tend to involve systems with interactions. To highlight the importance of interactions, let us first consider the case of noninteracting particles. The canonical example here is the ideal gas, which is composed of classical point-like particles that do not interact with each other. Because they do not interact, the motion of the particles is independent; if we want to know the energy of any particle, it is easy to calculate from its speed (E = mv22). The behavior of the whole system can be described by an ensemble of independent single particles. When the particles are interacting things are very different. Instead of an ideal gas, let us consider a gas of classical electrons interacting via the Coulomb force 1∕r. For two electrons the equations of motion can be solved analytically, but in a solid there are 1023 electrons (for all practical purposes, we can round 1023 up to infinity). To write down the energy of of one of them, we must account for the position of every single other electron. Thus the energy of just one electron is a function of 3N variables. Even with just three particles, analytic (pen and paper) solutions are impossible in most cases. An analytic solution for the motion of 1023 electrons is impossible, and “it’s not clear that such a solution, if it existed, would be useful” [6]. This is many-body physics. Instead of following individual particles, we describe their collective motion and the resulting emergent phenomena such as quasiparticles and phase transitions. Consider waves crashing on the beach. It would be foolish to try to understand this phenomenon by following the motion of all the individual water molecules. Instead, we can treat the water as a continuous substance with some emergent properties like density and viscosity. We can then study the waves as excitations the ground state of the water (the state without waves).

[1] This definition distinguishes condensed matter from particle physics (the other broad subdiscipline of physics), which is the ‘study of really hot and really fast-moving objects.’
[2] In practice, condensed matter tends to be the term used to describe physics that does not fit into one of the smaller, more well-defined subdisciplines like high-energy physics or cosmology.
[3] Both transistors and atomic clocks are essential to cellular telephones and satellite navigation systems like GPS.
[4]This quote is taken from “More is different” Science 177, 393 (1972) by P.W. Anderson , an excellent refutation of reductionism and discussion of emergent phenomena written in a manner that should be accessible to non-physicists.
[5] I hope to post non-technical descriptions of phase transitions and quasiparticles at some point in the future.
[6] Chaikin and Lubensky, 1998, p. 1

figure 4 from the paper

New paper: “Metamagnetism and zero-scale-factor universality in the two-dimensional J-Q model”

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.