Haldane on the second quantum revolution

This week I attended a great public lecture by Duncan Haldane: "Quantum Mechanics After One Hundred Years, and the 'Second Quantum Revolution' Today"

Starting from the discovery of quantum mechanics, he explained how the concept of quantum entanglement is fueling today's second quantum revolution and its connection to his Nobel Prize-winning work.

Haldane remarked that his work on quantum spin chains was controversial. He had theorists accosting him at conferences arguing he was wrong. These kinds of disputes among theorists are best settled by experiment. Undoubtedly, Haldane would not have received his Nobel Prize if his predictions had not been validated by experiments. How can you motivate some experimental group to be interested in your theory? If it generates controversy!

Similarly, experiments often are the drive for fresh theoretical advances. For example, the experimental discovery of the quantum Hall and fractional quantum Hall effects came before the theoretical predictions or understanding. 

A good example of this is a second important work by Haldane also cited in his prize: quantum Hall effects in absence of Landau levels. This now-seminal work went largely unnoticed for a decade, because the model based on a two-dimensional honeycomb lattice seemed unfeasible to realize in an experiment. Later, the unanticipated work experimental isolation of graphene drove theorists to this fresh area. Haldane's early theory work was recognised as the foundation for the discovery of time reversal-symmetric topological insulators and the whole "zoo" of topological materials that followed.

Haldane also emphasized the importance of luck in making ground-breaking discoveries. von Klitzing was not the first person to attempt quantum Hall measurements, but previous attempts had used a different experimental setup: varying current with a fixed magnetic field. Imperfections in the current source led to fluctuations in the measured resistivity, which seemed to be consistent with previous approximate theoretical calculations based on perturbation theory. von Klitzing's approach of measuring resistivity as a function of magnetic field strength, with current kept fixed, led to unexpectedly precise quantization which needed new theory to explain. 

Haldane's take-home message was thus: anyone can win a Nobel Prize, but you need luck and the perseverance to defend your work if it is challenged.

An earlier iteration of this talk is available here. A more detailed write-up is available here. 

   

2025 in review

I was sad to hear that my former workplace, the Center for Theoretical Physics of Complex Systems, is winding down. It was such a great academic environment with time to think and ample opportunities to learn from colleagues and the regular seminars and international workshops. From the Center's last Scientific Report:

Outlook: The center counts 492 publications, a total of 12813 citations, and an h-index h = 56 on Google Scholar. Despite its tremendous success, a continuation with a new division headed by a new director could not be realized by IBS, which is a pity and raises other IBS related questions which are not part of the current report. As a result of the foreseeable retirement of the current director, the PCS is winding down by the end of 2025. Practically all members of the PCS quickly found or are successfully securing new positions in research institutes and universities worldwide. The successful concept of the PCS will continue to exist through its alumni who carry the message into the world. These include twenty three (23!) faculties worldwide, including eight (8!) in Korea, six (6!) in China, and five (5!) in India, but also in Singapore, Vietnam, Brazil, USA, and the Philippines.

It's a real shame, especially since support for similar theory-focused research centers is so limited. Short term grants promote "safe" topics rather than giving researchers the time and freedom to follow their curiosity and try new ideas.

Looking back, memorable moments at PCS include:

• A visit and seminar in 2018 by J. Michael Kosterlitz in which he recounted his unusual journey to his Nobel Prize-winning work, including the important role played by job rejections and rock climbing. We didn't record his talk, but what seems to be a similar version can be found here.
• Workshop weeks, particularly the ability to sit in on workshops beyond one's own areas of expertise and get a first-hand glimpse of how informal interactions differ between different fields. Sometimes the welcome reception and evening activities would wind down within an hour or so, other times they would continue into the early morning, prime time for forging new collaborations and hearing important gossip. This is also why online conferences are a poor substitute for in-person events. 
• We went through a period where we were required (as a government institute) to have personal identifying information in all job applications be anonymised, to eliminate bias in their evaluation. Whoever came up with this didn't understand you cannot anonymise academic CVs - the publication list will inevitably give the name away!

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Physical Review A saw a significant increase in submissions, including some LLM-written papers. When used properly, LLMs can be a great productivity enhancer, particularly for non-native English speakers. On the other hand, if one uses the LLM to "cheat" and write the paper entirely, it is really easy to spot. Some dead giveaways: formatting, em-dashes, fake references, overly wordy text that doesn't say much (or makes no sense at all). 

For similar reasons it is easy to spot when a referee report (or student homework assignment) has been prepared using an LLM instead of real intelligence! During one of my classes this year, I was sad to see some students completing their hand-written humanities assignment by directly copying the output from ChatGPT. At the end of the day, tedious "homework" like unpaid reviews are not just a box to tick off, they are exercise for your mind. By looking carefully for flaws and inconsistencies in someone else's work, you are also developing the critical thinking skills that will improve your own writing and research. Don't short-change yourself by delegating to an LLM!

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My own research is going at a slower pace. A lot of thinking time has been replaced with grant-writing. I hope to see some payoff for this substantial effort in 2026! 

Michael Berry on the next century of quantum mechanics

Prof. Michael Berry talked about his work and the future of quantum mechanics in an interview during his recent visit to ICTS-TIFR for the ‘A Hundred Years of Quantum Mechanics’ program. Some excerpts:

Q: What is the status of the foundational questions in quantum mechanics now?

A: I have no idea, I don’t work on them. [...] Transport the question back to classical mechanics. Two points. Is Newton’s equation more fundamental than Hamiltonian’s? Philosophers could argue about it. In fact, Newton’s equations are more general, that’s another matter. 

This refers to work by Berry and others on curl forces: position-dependent forces that cannot be written as the gradient of a potential. Curl forces have many peculiar properties - symmetries do not imply conservation laws, the dynamics are non-conservative yet non-dissipative, and in many cases they cannot be generated by a Hamiltonian. I first heard about this fascinating topic when Berry gave a colloquium at NTU in 2016. There has been quite a bit of work on this topic since then, including a recent generalization to quantum curl force dynamics.

Q: Do you have any advice for people who work in this field or who aspire to work in this field?

A: Yes. I have two contradictory pieces of advice for people who ask me for career advice.

The first piece of advice is: don’t take advice.

But, if pressed, I would say that if I were starting out, I would probably work on quantum information. Probably, though I can’t tell — this is what philosophers call counterfactual history. So I would say: work on quantum information. There are so many riches to be uncovered there to do with these big Hilbert spaces, even with a modest number of particles. So that’s what I would say.

For context, Berry's main contributions to physics relate to the "simple" case of linear wave equations and single particle quantum mechanics - well-established theories that nevertheless held numerous surprises and emergent behaviour in their singular limits and asymptotic phenomena. We've only scratched the surface when it comes to exploring these effects in complex many-body quantum systems.

The full text of the interview can be found here.

 

 

 

Asian Network Mini-School on Quantum Materials 2024

Last week I visited the University of Indonesia to present two lectures on topological photonics at the Asian Network Mini-School on Quantum Materials 2024. This is one of a series of events held in South East Asian countries held by the ICTP Asian Network. The school attracted 95 participants from Indonesian universities, the majority being advanced undergraduates or graduate students. Meetings such as these provide valuable opportunities for early career scientists to learn about cutting-edge research areas and build collaborations with others in the region. I was impressed by the level of engagement from the audience - even though I ended my first lecture 20 minutes early, the remaining time was fully occupied by questions! Many thanks to the local organizers for putting together such an enjoyable meeting! Two more schools will be held this year, both in Thailand, on complex condensed matter systems and magnetism and spectroscopy, with more planned for next year.

Mistakes to avoid when writing the introduction to your paper

As a journal editor I read a lot of manuscripts. The introduction is often the hardest part of a paper to write, particularly for high impact journals where one must tread a fine line between shameless self-promotion and clearly explaining the importance of one's work in a manner that is appreciated by both specialists and non-specialists. Two mistakes crop up time and again:

Mass citations

"Extremely niche topic x has become a hot topic due to its potential applications [1-26]. Many novel effects have been reported [27-48]. These works have been extended to unprecedented directions [49-68], paving the way to..."

Yes, it is important to acknowledge relevant prior work on your topic. But when you cite papers en masse it gives the impression that you don't understand which papers in your research paper are really important!

 One sentence citations

 "Smith et al. explored applications of extremely niche hot topic x [1]. Brown et al. innovatively demonstrated a novel effect [2]. Newton et al. paved the way to...[3]."

 The opposite extreme of explaining each reference individually (but in a single sentence only, otherwise the introduction will be too long) has the same effect, suggesting you have merely skimmed the works you have cited without really understanding how they fit together and what the bigger picture is.

 

Don't do this! Cite one or two review articles instead, along with the specific works you are building on. Don't make the reader have to do a literature review just to tell whether your paper might be worth reading!

Reading the right papers

Students often find it particularly hard to tell which papers are worth an in-depth reading, which can be skimmed, and which are not essential to the current research project. Since this is something that is usually only learned through experience, examples can be helpful for building intuition.

Consider the first paper from my PhD research, Pseudospin and nonlinear conical diffraction in Lieb lattices, published in Physical Review A. With the benefit of hindsight, this turned out to be a Good Paper, with multiple experimental groups exploring some of the ideas in the following years. Why did it have an impact?

The research project didn't start by reading a bunch of papers and getting a new idea. The idea arose from talking to people - experimental collaborators, and one of the eventual co-authors (Omri), who had recently finished his PhD on the theory of wave propagation in graphene-like honeycomb photonic lattices. 

I was asked to see whether any of the ideas in his thesis could be feasibly investigated by our experimental collaborators. Honeycomb lattices being hard to do in their setup at the time, they wanted to know whether similar phenomena might be observable in a square lattice. Similar to how one can remove a period-doubled lattice from the triangular lattice to create a honeycomb lattice, removing sites from an ordinary square lattice yields a face-centred square lattice with intersecting bands. Great!

As is so often the case in research, we were not the first to have this idea, and actually in the preceding few years several groups had been exploring the properties of this lattice, motivated by huge interest in the electronic properties of graphene (Refs. [7,8,10,11,12,13] in the paper). These works were all published in the Physical Review, not "high impact" venues such as Nature / PRL, probably because referees thought it would be difficult to reproduce this model in an experiment. Being background material, an in-depth reading of all these papers was not required - we just needed to know roughly what they did and how they did it to understand how novel our results were.

In these papers we not only found the now commonly-used name for this lattice (the Lieb lattice), but also learned about how its properties were of interest in the context of cold atoms / BECs and electronic properties of materials. Lucky for us, we could not find any papers studying this lattice from the point of view of photonics, meaning that we had something novel! But on the other hand, we clearly couldn't just take these existing results (based on tight binding models) and do exactly the same using a "photonic" tight binding model without our work ending up being merely incremental and forgettable. Therefore we considered a few photonics-specific extensions:

(1) Wave propagation dynamics in the nonlinear regime, translating the analysis in one of Omri's recent papers (Ref. [11]) to the Lieb lattice setting. This one I had to read and re-read in detail to fully understand the analytical and numerical simulation tools used.

(2) Understanding the coupling between the different angular momentum degrees of freedom in our system. This similarly involved an extension of previous results by others for the honeycomb lattice (Ref. [18]) to the Lieb lattice setting. We also had to carefully read and understand this paper.

(3) Photonics-specific simulations not limited to a tight binding approximation and using experimentally-feasible parameters similar to those used in our collaborators' recent work (Ref. [26]).

In summary:

• Talk to experts early on to find out what the real important problems are and whether they have any that you are in a position to solve.
• Once you have an approximate solution or plan of attack, you need to check the literature to understand its importance and relevance to other work. At this stage you will often encounter papers with ideas very similar to yours.
• Identify your niche and expand on the novel points of your work, usually building on a few specific related papers that need to be carefully read and understood.
• It is usually easier to first solve a specific problem a single expert is having, and then figure out how your solution generalizes. The reverse approach - solving a problem in generality before considering specific examples - should only be attempted with extreme caution.

Doing literature reviews the smart way

Despite literature surveys being a key component of research, strategies for reviewing the scientific literature and identifying promising avenues of research are rarely included in graduate student coursework. This means that students may be unaware of more powerful tools that are available.

It is useful to have a tiered search strategy, starting with resources aimed at a broad audience, for example technical magazines such as Optics & Photonics News, to identify interesting or promising directions to study in more detail. While wikipedia is a popular first choice, peer-reviewed alternatives such as Scholarpedia provide more reliable and trustworthy articles written by known experts.

Google Scholar is perhaps the most popular scholarly search engine, but its limitations mean it is most useful for exploring papers on highly specific lines of research, mainly by following citation trains and highly-cited papers. Subscription-based search engines such as Web of Science are usually available under university subscriptions and give much more powerful tools for exploring a research area and seeing the bigger picture, such as the ability to filter search results by journal or author affiliations and visualise how publication trends are evolving over time using citation reports

Thanks to covid, many academic talks can now be viewed online. These are a great alternative to reading the papers themselves, particularly because the speaker may reveal insights that didn't end up in the journal article. One should keep in mind differences between workshops and larger conferences - target audience, breadth and depth of individual talks and the programme as a whole, and sometimes the candour of the speakers, particularly if the talk will be made available online. This means that in-person conference attendance is still highly valuable, because speakers may be more willing to share unpublished work and future research ideas during smaller more informal discussions. Talking to the right person can save hours of time figuring out what the key references are!

The volume of publications in an area may shape your research strategy. If a given keyword has hundreds or thousands of articles coming out each year, it's usually a sign that you need to narrow your focus to find a niche in which you can shine. Publications often follow a hype cycle, that is, an initial surge of interest leading to a transient peak in activity, followed by a more stable plateau as the field matures. Sometimes a line ends up being infeasible, leading to interest dying off before such a plateau can form.

It is important to emphasize the number of publications in an area should not be used to judge whether a field is worthwhile to study. For example, one researcher might see a booming field and be put off, desiring to work in a smaller area with a better potential for growth. A short peak of activity followed by little interest may suggest a research line has a difficult problem that nobody knows how to solve, offering an opportunity for you to make your mark.

Does artificial intelligence have a place in reviewing the literature and deciding on promising lines of research? Yes and no. Artificial intelligence is more than just large language models and chatbots, encompassing a variety of other machine learning-based tools for enhancing productivity, for example by helping to analyse and visualise citation networks. Some experimental examples of these network analysis tools are available on arXiv through arXivlabs and are worth a try - even if their capabilities are limited or inaccessible today (e.g. requiring a subscription), in the coming years the best ones will become more widely available via university-wide subscriptions, similar to the growth of collaborative paper-writing tools such as Overleaf.

And what about large language models? In my opinion, it's best to avoid them when carrying out literature reviews. Language models are trained to favour fluency over accuracy, so rather than generating new knowledge they are better used for performing tasks where the end-user can verify the output. Even when asked to analyze specific papers, you can't be sure that the model missed or misunderstood an important point, for example when jargon used within a research area differs from the commonly-understood meaning of a word. And even if (or when) these issues are solved by new and improved models, at the end of the day large language models are designed to spit out probable-sounding sequence of tokens. On the other hand, scientific breakthroughs often come about through the pursuit of unlikely or unexpected avenues of investigation.

Finally, one should not read too much. Too much time spent reading what other people have done not only takes time away from your own research, but it can also sap your creativity and ability to pursue directions away from the groupthink. Richard Hamming explained this eloquently in famous lecture "You and Your Research" he gave at Bell Labs, available both as a text transcript and a video recording. I highly recommend reading or watching!

In summary:

1. You should use a variety of sources, search engines, and media types
2. Remember every source and search engine has a bias
3. Aggregated statistics are just as important as individual papers
4. Try emerging AI-powered search & visualization tools
5. Don't read too much!