Category Archives: paper

Title page of Ising model paper

Just published: field-stabilized frozen states in the AFM Ising model

Leave a reply

I’m thrilled to announce that my first single-author paper has just been published in Physical Review E:

Field-induced freezing in the unfrustrated Ising antiferromagnet
Adam Iaizzi,
Physical Review E 102, 032112 (2020) [paywall] 
[free PDF] [arXiv]

This paper is a continuation of the theme of my research career, which could be loosely described: “try adding a magnetic field to an antiferromagnet and see if something interesting happens.” In this case, I added a magnetic field to the classical 2D Ising antiferromagnet and studied it with the simplest implementation of Monte Carlo: the Metropolis(-Rosenbluth-Teller) algorithm. At low temperatures I found that simulations never reached the ground state. Instead, they get trapped in local energy minima from which they never escape: frozen states with finite magnetization. There are so many of these frozen states available that you are effectively guaranteed to cross one before you can reach the correct ground state. These frozen states can be described by simple rules based on stable local configurations.

Continue reading →

Spinons: what are they and what do they do?

Leave a reply

Updated 2020-03-22

One problem with scientific publishing is that the most up-to-date information about a topic is spread out across numerous extremely technical journal articles, none of which explains the concept from scratch. In response to a request from a friend (see previous post), I thought I would take a little time to try to answer the question: “what is a spinon?”

Continue reading →

Just presented at the Annual Meeting of the Physical Society of Taiwan

Leave a reply

I just presented a talk “Quenching to field-stabilized magnetization plateaus in the unfrustrated Ising antiferromagnet” based on my preprint that I posted on arXiv last week at the Annual Meeting of the Physical Society of Taiwan at National Pingtung University in Pingtung, Taiwan. I haven’t gotten around to making a post about this paper yet (that is coming soon), but in the meantime I will post my slides from this talk here. My slides included some movies of the process of freezing in to magnetization plateaus. Since PDFs can’t include movies I will post the movies below.

Gif of Ising spin configurations arriving at a frozen plateau state.
The spin configuration over time starting from a random (T=∞) state and doing single spin flip Metropolis updates at T=0 and h=1 until we arrive at a final frozen state. Individual spin states are denoted by the (+) and (-); the background shading shows which of the antiferromagnetic ground states each site is in. In the final frozen state the domain walls are all straight lines or corners with (+) on the inside.

Gif of Ising spin configurations arriving at a frozen plateau state.
The spin configuration over time starting from a random (T=∞) state and doing single spin flip Metropolis updates at T=0 and h=3 until we arrive at a final frozen state. Individual spin states are denoted by the (+) and (-); the background shading shows which of the antiferromagnetic ground states each site is in. In the final frozen state the domain walls are all diagonal or square-wave-like with excess (+) spin.

Footnotes and citations should look different

1 Reply

Overall, I think physics is lucky to have its premier journals (Physical Review) be run by our own nonprofit professional society—APS. I think that explains, at least in part, why the arXiv has been so successful in physics and why similar efforts have floundered in other fields.

All that said, I have one bone to pick with the Physical Review journals: they insist that footnotes should be denoted in the same manner as citations [1,2]. Citations and footnotes serve very different purposes, and I both use and consume them in very different ways. When I’m reading a paper, I often read the footnotes, especially if I’m trying to totally understand a passage. I almost never look at the citations on my first reading. As a reader, I love footnotes! They’re a great way to add context, clarifications, parenthetical remarks, or definitions without interrupting the flow of your argument. Citations, on the other hand, are for backing up your claims or giving proper credit. If you mistake a footnote for a citation, you might miss some useful information or you might wrongly assume that the claim is backed up elsewhere in the literature [3]. Finally, I prefer footnotes to endnotes because footnotes keeps the information nearby, rather than forcing readers to flip pages back and forth.

In summary, Physical Review Letters and A, B, C and D: please follow Physical Review E‘s lead and allow separate footnotes!

Just one section called references:

[1] Waldron et al. “The Physical Review Style and Notation Guide” APS 2011 (a citation)
[2] At least for Physical Review B and Physical Review Letters, which are the PR journals I use. Phys Rev E does allow separate footnotes. (a footnote)
[3] For example, if you mistook [2] for a citation, you might not have noticed my caveat about which specific journals exhibit this problem.

Update 2020-03-12

Let the record reflect that after I posted this I heard that PRB does, in fact, allow separate footnotes. I tested this with my most recent paper and I now have experimental proof.

New paper: Bose-Einstein condensation of deconfined spinons in 2D

1 Reply

My new paper, Bose-Einstein condensation of deconfined spinons in two dimensions, is finally live on arXiv! (arXiv:1909.01594)

Context

Almost all phase transitions are described by a theory known as the Landau-Ginzburg-Wilson (LGW) paradigm, which describes the phase transition in terms of an order parameter that also describes the ordered state (e.g. a transition to a ferromagnet is described by the magnetization). There is therefore great interest in find examples of phase transitions that do not obey this paradigm. Growing numerical evidence suggests that the transition between the Néel antiferromagnet (AFM) and valence-bond solid (VBS) in certain quantum magnets may be such a transition. Since the Néel AFM and VBS break unrelated symmetries (SU(2) and Z4), LGW predicts the transition between them will be first order. Extensive numerical studies, however, strongly suggest that it is continuous. Instead, this transition appears to be described by deconfined quantum criticality (DQC).

In DQC, the critical point is not described by either order parameter, but instead by emergent fractionalized excitations, in this case spinons, which are spin-1/2 bosons (crazy, right?). Away from the critical point spinons are confined inside conventional magnon excitations (like quarks in a proton), but at transition they deconfine. The existence of deconfined quantum criticality remains controversial.

In this paper…

… we add a magnetic field to the DQC point to produce a Bose-Einstein condensate (BEC) of magnetic excitations and use thermodynamics to determine if they are spinons or magnons. My collaborators, Harley Scammell and Oleg Sushkov, developed a quantum field theory approach to predict the low-temperature behavior of a spinons in a magnetic field. We found that the field causes the spinon behavior to differ dramatically from magnons. Using my numerics, we show that the magnetic excitations we observe must indeed be bosonic spinons. This constitutes the first evidence for a BEC of spinons and provides more evidence for DQC theory.

Abstract

The transition between the Néel antiferromagnet and the valence-bond solid state in two dimensions has become a paradigmatic example of deconfined quantum criticality, a non-Landau transition characterized by fractionalized excitations (spinons). We consider an extension of this scenario whereby the deconfined spinons are subject to a magnetic field. The primary purpose is to identify the exotic scenario of a Bose-Einstein condensate of spinons. We employ quantum Monte Carlo simulations of the J–Q model with a magnetic field and perform a quantum field theoretic analysis of the magnetic field and temperature dependence of thermodynamic quantities. The combined analysis provides compelling evidence for the Bose-Einstein condensation of spinons and also demonstrates an extended temperature regime in which the system is best described as gas of spinons interacting with an emergent gauge field.

I was walking by the SpringerNature booth at the March Meeting and the agent I worked with (Sam Harrison) pointed out that a print copy of my dissertation was there, on display and for sale! Truly a surreal experience!

Me and my dissertation on display at the March Meeting

Me and my dissertation on display at the March Meeting. Thanks to Sam Harrison for taking this picture for me.

My dissertation is now available online from Springer!

2 Replies
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

Leave a reply

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.