What is your experience of using AI for research in condensed matter theory?

 I have been dabbling a little with using AI (at a very basic level) to help me with some research problems. For example, in a recent preprint, I did the maths in the Appendix with help from AI.

I am curious to hear from the experience of others of using it for research in condensed matter theory and theoretical chemistry. 

Peter Woit made a similar request to the high-energy theory community. The responses are helpful and worth reading. An earlier post about AI in math drew the following concrete suggestions from "Greg"

"In math, one thing I found useful to get my bearings was to go through some of my published papers and ask it to try and improve the main result.

Another is to do an adversarial audit of a paper you are very familiar with (yours if you have the stomach for it, someone else’s if not) and then see which of the complaints are pedantic and which are actual.

A third is to give you a history and references/citations for an argument that it provides.

A fourth is to suggest different ways to simplify an argument, even if they are only half-formed in your mind or if you are having trouble making them precise. (Try to be as precise as possible, but don’t use the same filter that you would use with a colleague. Sometimes vague is the best you can do.)

If you are thinking of proposing a question or conjecture in a grant application or preprint, ask it to stress test the conjecture. Don’t lean too much in one direction when prompting it and asking repeated questions (unless there is a particular thread you are trying to untangle, the use your nose, of course), but try to have it explore the positive direction in one query and the negative direction in a follow-up."

[A year ago, I posted about a benchmarking paper for condensed matter theory. I have not seen any updates on that work. For example, have the latest AI models improved significantly on these benchmarks?]

About a month ago, my office mate, Henry Nourse, gave a nice talk, "Is my skillset safe in an AI future?" at the UQ Condensed Matter group meeting. Henry gave a very concrete example of how he used it for a problem involving Raman scattering from quantum spin chains.

Henry stimulated me to see whether AI could help with a problem I was struggling with. It was basically a mathematics problem involving a Fourier transform. There were things that I thought were probably true, but after days of messing with algebra, my aging brain could not prove them. Google Gemini gave the answer in less than a minute. On the one hand, that is impressive. On the other hand, the absolute key was knowing precisely what question to ask it and knowing whether the anwer made sense. Furthermore, it took hours for me to check the result and to refine it, sometimes through further prompts. Besides getting the result, a nice benefit is that AI can quickly generate a LaTeX file that describes the mathematical argument and provides relevant references. Nevertheless, there are still hours more work of checking and polishing the text.

[Aside. The proof made use of various Bessel function identities that I had forgotten. I had used them extensively in a paper about thirty years ago.]

This success motivated me to use Google Gemini to develop, start to solve, and analyse a "simple" classical two-dimensional model of springs interacting with Ising spins. It is simple enough that I think most of the analysis can be done analytically. I have been working on related models on and off for the last couple of years. However, again due to my aging brain, I often get stuck on algebra or the subtleties of the theory of elasticity. AI does the algebra quickly. Furthermore, all the equations are formatted in LaTex. Great!

Again, it bears repeating that a thorough knowledge and intuition about the underlying physics is probably essential for knowing what prompts to make, and whether the answers make sense and are useful. The fact that I had struggled with related models offline beforehand really guided my interaction with AI.

Again, everything still needs to be checked. Sometimes AI makes suggestions that I think may be "hallucinations" [e.g. suggesting connections to the Svetitsky-Yaffe conjecture for lattice gauge theory] that may have arisen from earlier questions about unrelated topics. When I ask similar questions on a later day, it sometimes gives a different answer. For example, once it neglected to include the effect of one term in the Hamiltonian.

Initially, I struggled to keep records and manage the workflow. Eventually, I found it helpful to have a single LaTex file which is like a rough draft of a paper, into which I insert results. I found my engagements with AI both interesting, stimulating, and stressful. I now limit my sessions to short periods of time and then polish and edit the LaTex document in between sessions. This helps me consider what the next steps are. I am glad I am retired and can do all this at a leisurely pace.

What I am doing is incredibly basic compared to what may be possible. I am just using the free version of Google Gemini.

My limited experience raises all sorts of questions about the potential and pitfalls of graduate students using AI in research. Will it enhance or hinder their education? Potentially both?

There are some great quotes from Terence Tao in a recent New York Times article

“The effort needed to solve problems [without AI] is often very instructive. It teaches you something. It’s like going to the gym and having a goal to lift a weight a hundred times. Now, A.I. can solve questions without really getting any value out of them. It’s like having machines that can lift weights for you at the gym.”

“It feels to me like a really clever student who has memorized everything for the test but doesn’t have a deep understanding of the concept,..”

“This has some value,... But once someone shows a specific path to the waterfall, people just take that path. They don’t spend as much time looking for other paths.”

I also recommend Tao's recent lecture at the International Congress of Mathematicians.

For now, I would love to hear from others, particularly in condensed matter theory or theoretical chemistry.

What do you use AI for? What have you learned from the experience? How do you go about it? For example, how do you decide what prompts to use? How do you manage workflows? How do you document your work? What is it good at? What is it bad at? What potential benefits do you see? What pitfalls?

What is so amazing about the Fermi energy?

In two weeks, I am giving two lectures about degenerate Fermi gases in a third-year undergraduate course on statistical mechanics. The textbook is the beautiful book by Schroeder.

I want to highlight a few things that are amazing about the Fermi energy.

1. It is given by an incredibly simple expression.

E_F =

ℏ²

2m

(3π²n)^2/3

2. Besides fundamental constants, it is only determined by the number density of fermions n.

3. It is relevant to diverse systems: electrons in a metal, liquid 3He, electrons in a white dwarf star, neutrons in a neutron star, ultracold fermionic atoms such as 6Li. The table below shows that for all of these systems many of them are in the regime where the temperature is much less than the Fermi temperature. In other words, the Fermi energy (temperature) is so "large" that "low" temperatures can be very "high". 

4. Quantum effects can occur at surprisingly high temperatures. Most experiments that probe quantum effects are performed at low temperatures, often on the scale of a few Kelvin, or even less. Yet, inside a star, the quantisation of energy levels and quantum statistics can dominate the physics of the system, even at temperatures of millions or billions of Kelvin.

Note, how the temperatures of these systems span 18 orders of magnitude!

System	Typical Number Density (n/V)	Typical Temperature (T)	Fermi Temperature (TF)
Electrons in a metal	~1022 – 1023 cm-3	~300 K (Room temp)	~5 × 104 K
3He atoms in liquid 3He	1.6 ×1022 cm-3	< 1 K (Cryogenic)	~2 – 5 K
Nucleons in atomic nuclei	1.6 ×1038 cm-3	~0 K (Ground state)	4.4 × 1011 K
Electrons in a white dwarf star	~1029 – 1030 cm-3	~107 K (Interior)	~108 – 109 K
Neutrons in a neutron star	~1038 – 1039 cm-3	~108 – 109 K	~1011 – 1012 K
Fermionic atoms in an ultracold gas	~1012 – 1014 cm-3	~10 – 100 nK	~100 – 1000 nK

The table was made with Google Gemini.

Two asides.

A. An old blog post considered the interesting question of why people call these systems "degenerate."

B. A more profound question is why neglecting the interactions between the fermions (which involves energies comparable to the Fermi energy in most of these systems) can give a theory that is so successful, both qualitatively and reasonably quantitatively. Landau's Fermi liquid theory provides the answer.

The subtlety of elastic interactions in spin crossover materials

My collaborators and I recently posted a preprint

Exact mapping from short-ranged harmonic elastic models of spin crossover materials to Ising models with interactions at all length scales

Nadeem Natt, Gian Ruzzi, Jace Cruddas, Ross H. McKenzie, Ben J. Powell

Spin crossover (SCO) materials are reversible molecular switches found in a wide range of transition metal complexes and metal organic frameworks (MOFs). They exhibit diverse spin state orderings and transitions between them. Here we present an exact mapping from harmonic elastic models to Ising-like models with both a short-range Ising interaction that decays with a power law at large distances and a long-range (infinite-range) Husimi-Temperley interaction that is independent of distance. We apply this mapping to a simple model of SCO frameworks. This provides a microscopic justification for an Ising-Husimi-Temperley model description, which has previously only been justified on phenomenological grounds. Elastic frustration is required for non-zero Ising interactions, but whether or not the short-range interactions in the Ising model are geometrically frustrated depends on the ratio of the bulk and shear moduli, or equivalently Poisson's ratio. The long-range interaction has two origins: (i) a self-interaction on the average spin state, mediated through the coupling between the average spin state and the unit cell parameters; and (ii) an infrared divergence in the spin state-spin state coupling mediated by displacements of metals and ligands within the unit cell. In the absence of elastic frustration these terms are equal and opposite so there is no long-range interaction. However, in general they do not cancel and there is a long-range Ising interaction. The long-range interaction is independent of the distance between metal centers, nevertheless it leads to an extensive contribution to the (free) energy. In this model the Husimi-Temperley interaction dominates transitions of spin states, whereas multistep transitions and intermediate order are observed if only the pure (power-law) Ising interaction are retained, only single-step transitions are found in the full model.

The paper has a long history. The original version was posted six years ago! 

Our earlier derivation of the effective Ising model was incorrect as it did not take into account subtle boundary effects that lead to an infinite-range Ising interaction. This significantly changes the phase diagram of the model. For example, multi-step spin state transitions do not occur. 

It required a new generation of graduate students to redo the calculations and finish the paper. 

The paper also includes a first for me. I did the derivation in the Appendix with AI (and checked by a human). This experience showed me both the potential and pitfalls of AI in my research. More on that later.

Senior position available in sunny Australia

I am retired but still have some involvement with the School of Mathematics at the University of Queensland, in sunny Brisbane, Australia. It was employed for two decades there. 

Brisbane is one of the most liveable cities in the world. I love all the hiking nearby.  Australia has national health care, compulsory voting, strict gun control, and the world's first ban on social media for children...

A colleague asked me to post the advert for the position of Professor and Head of School, School of Mathematics and Physics

It might be attractive to a senior faculty member in the USA with management experience who wants to escape the current challenging environment in the USA. For such a person, an earlier post may provide some relevant advice and context.

What does this movie tell us about the modern university?

Last night, my wife and I watched the movie, Wit.

You can watch the full movie here (free with ads). I should warn that some of the content is quite disturbing and confronting.

I asked Google Gemini the following question:

"the movie wit, starring emma thompson, features two professors, one of oncology and another of english literature. the latter has terminal cancer. in spite of their academic credentials, neither seems equipped to cope with the human side of the suffering of the patient. alisdair macintyre was a critic of the modern university. what might have he said about this movie?"

Here is the answer.

"Alasdair MacIntyre, a prominent critic of the modern university and contemporary moral culture, viewed modern institutions not as communities dedicated to a shared human good, but as bureaucratic structures driven by specialization, technical expertise, and managerial effectiveness.

Based on his philosophical framework—most notably developed in After Virtue—MacIntyre would likely view the dynamic in the movie Wit as a quintessential illustration of the moral and intellectual failures of the modern university. Here is what he might say about it:

1. The Triumph of Bureaucratic Expertise Over Human "Telos"

MacIntyre argued that modern academic disciplines have abandoned any coherent notion of a unified human telos (purpose or ultimate goal). Instead, they have fractured into compartmentalized technical specialties.

• The Oncologist: Represents the epitome of modern "technocratic" or "managerial" expertise. To the hospital and the university, medicine is treated as a problem-solving science rather than a moral practice aimed at human flourishing. The patient is reduced to a data point, a mechanical puzzle, or a vehicle for research.
  
  
• The English Literature Professor: Though her field deals with the humanities, the modern study of literature has similarly grown hyper-specialized, detached, and academicized (focused on obscure analysis, such as John Donne’s holy sonnets, rather than wisdom or existential truth).
  
  

2. The Failure of Emotivism and Detached Rationalism

MacIntyre famously claimed that modern moral discourse has devolved into emotivism—the idea that ethical judgments are merely expressions of personal preference or feeling rather than rational truths.

• Neither professor is equipped to handle human suffering because their education has stripped them of a shared moral language.
  
  
• The literature professor spent her life analyzing deep themes of mortality and grace on paper, but because modern academia treats texts as objects of clinical critique rather than guides for living, she remains entirely unprepared to face her own mortality with actual grace. Her knowledge was purely aesthetic and intellectual, leaving a void where real moral virtue should be.
  
  

3. The Loss of Genuine Community

For MacIntyre, universities were historically meant to be traditions-based communities focused on cultivating virtues.  He viewed the modern university as having traded this for bureaucratic careerism and bureaucratic compartmentalization.

• In Wit, the coldness of the hospital-university complex highlights a complete absence of genuine human community. Interactions are transactional and analytical.
  
  

In short, MacIntyre would likely argue that Wit demonstrates the tragic irony of the modern academy: it produces hyper-competent specialists who know an immense amount about narrow subjects, yet are entirely illiterate in the art of being human."

That is a beautiful reflection. My enjoyment of it is somewhat overshadowed by my awareness that AI produced it. It also raises all questions about how to use AI in ways that do not diminish my own humanity.

Statistical mechanics in just one equation

 This semester, I am giving four lectures in a third-year undergraduate course on statistical mechanics. Last year, I gave a guest lecture on the Ising model.

The first thing I want to emphasise is that the whole course is built around just one equation.

exp(−F(T, V)/kT) = ∑_s exp(−E_s/kT) ≡ Z(T, V)

This connects macroscopic thermodynamic properties (contained in the Helmholtz free energy F(T,V)) to microscopic properties (the energies E_s of all possible states s of the system).

[Note that from equilibrium thermodynamics, partial derivatives of F(T,V) give the entropy (and specific heat capacity) and the pressure (equation of state)].

I think that we are so used to this equation that we may miss just how amazing and profound it is.

First, the equation is incredibly simple.

Second, it is universal. It applies to any system in thermodynamic equilibrium regardless of its chemical or physical composition.

Third, in the context of the theory of emergent phenomena, it is exceptional because it provides a robust, tested way to connect the microscopic to the macroscopic. Biology, neuroscience, economics, sociology, and computer science have nothing like it.

Fourth, although the above three points are impressive, the basis of its validity remains an outstanding problem (a mystery?). One can "derive" it and "justify" it by drawing on assumptions such as the fundamental postulate ("in an isolated system all accessible microstates are equally probable"), the principle of maximum entropy, and the validity of equilibrium thermodynamics. But why are they true?

Although the equation is simple, implementing it, particularly for systems of interacting particles, is challenging. This challenge can be broken into five steps. One can get stuck on any one of the steps. People build whole careers on them.

1. For a system of interest, propose microscopic states of each particle and a Hamiltonian for the whole system.

2. Enumerate all possible microscopic states of the system.

3. Evaluate the energy of each of these microstates.

4. Perform the sum over all states in the partition function Z.

5. Take the thermodynamic limit where the system size becomes infinite.