Money and more is different

Phil Anderson's classic article, "More is different" from 1972 has a somewhat humorous and enigmatic ending.

In closing, I offer two examples from economics of what I hope to have said. Marx said that quantitative differences become qualitative ones, but a dialogue in Paris in the 1920's sums it up even more clearly: 

FITZGERALD: The rich are different  from us. 

HEMINGWAY: Yes, they have more money. 

So, what is this all about? What is the background? 

According to an article in the Financial Times

There is an apocryphal tale about an exchange between two of America’s most famous novelists on the nature of wealthy individuals. F Scott Fitzgerald, author of The Great Gatsby, is reputed to have said: “The rich are different from you and me.” In reply, Ernest Hemingway is quoted as saying: “Yes, they have more money.” 

 As it happens, the quote attributed to Fitzgerald seems to be a corruption of a line in The Rich Boy, his 1926 short story: “Let me tell you about the very rich. They are different from you and me.”

With regard to Marx, as far as I can tell, the idea that "quantitative differences become qualitative differences" was discussed by Friedrich Engels in his unfinished 1883 work, Dialectics of Nature. The manuscript, drew on three "laws of dialectics" proposed by Hegel. The first law is

1. The law of the transformation of quantity into quality and vice versa. For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtraction of matter or motion (so-called energy).

An entry from the Great Soviet Encyclopedia illustrates the central role this "law" played in Soviet ideology, particularly in giving a "scientific" basis for the dialectical materialism at the centre of Marxist-Leninist philosophy.

A paper in PNAS in 2000 comments

Marx himself seems to have made only limited use of the explanatory power of the transition from quantity to quality. For example, in Capital, he noted “the correctness of the law discovered by Hegel … that merely quantitative differences beyond a certain point pass into qualitative changes,” and illustrated this process in the economic sphere by speaking of “the minimum of the sum of value that the individual possessor of money … must command to metamorphose himself into a capitalist …” (2).

Clarifying vision, strategy, tactics, goals, objectives, ...

 In any area of life, and particularly in science, it is important to know who you are, where you are, and where you want to head. This is true not just for individuals but also for institutions and communities. This then leads to discussions about mission, vision, goals, strategy, objectives, ... And as time passes how do you evaluate progress and adjust course? This is even more relevant today because the pandemic has upended so much.

Such discussion, and our thinking, can quickly become confusing because some of these terms mean different things to different people. Furthermore, it is easy to start conflating the terms. This is particularly unhelpful when "means and ends" and "inputs and outputs" get inverted, as when people become obsessed with metrics. For example, when the mission of a university becomes to rise in the global rankings or for an individual to increase their h-index, then things go pear-shaped.

Here I just want to try and clarify, partly for my own benefit, what all these different terms might mean, interacting with some of the literature out there. However, I should stress that there is no consensus on either the terminology or approach and it is not clear to me that there needs to be. Rather I think the most important thing is to have some sort of clear framework that is agreed upon by all the participants in these types of discussions. Note that it is hard to be completely precise with the definitions and the distinctions between them.

Mission: this is your identity and purpose (your passions, gifts, strengths, weaknesses, opportunities)

Vision: this is the future that you would like to see become reality

Goal: a concrete outcome

Strategy: the approach you take

Tactics: the short-term actions you take to implement your strategy

Objectives: things that can be evaluated to see whether your tactics are moving you forwards and your strategy is working. [Personally I think it is best is these are qualitative rather than quantitative, but perhaps that is an over-reaction to metric mania].

This figure is taken from a Harvard Business Review article 

How to Do Strategic Planning Like a Futurist by Amy Webb

The distinctions are best illustrated with concrete examples such as below.

Mission: this is your purpose and identity (your passions, gifts, strengths, weaknesses, opportunities)

Sarah is a theorist working at the interface of soft condensed matter and biological physics. She has tenure and works at a leading research university. 

Vision: this is the future that you would like to see become reality

To see a new scientific synergy between the cell biology and soft condensed matter communities. This synergy will be valued by both communities.

Goal: a concrete outcome

That a major open question in cell biology will be answered by the use of concepts and/or techniques from soft condensed matter. That cell biology would provide a new model system to be studied by soft condensed matter physicists.

Strategy: the approach you take

Play the long game. Learn. Educate. Be humble. Build trust, interest, and collaborations.

Tactics: the short-term actions you take to implement your strategy

Learn as much as possible about cell biology by reading and talking to cell biologists in her university. Attend their seminars and conferences.  Invite some cell biologists to give a physics colloquium and to attend Sarah's group meeting.

Objectives: things that can be evaluated to see whether your tactics are moving you forwards and your strategy is working

Get an unsolicited invitation to speak at a major cell biology conference. Build a local collaboration that results in one joint paper in the journal Cell and another in PRL. Get a joint NIH grant. For Sarah to have some of her papers from physics journals cited in Cell. To see several soft condensed matter concepts, results, and/or techniques described in an introductory textbook on cell biology.

What do you think? Is this helpful? Are there any particular tools or articles that you have found helpful?

Emergent quasi-particles and gauge fields in quantum matter

Unfortunately, there is a paucity of good review articles that give gentle introductions to current research in condensed matter, both for beginning graduate students and for curious non-experts. Too many reviews are exhaustive, in both senses of the word! Contemporary Physics is a journal that aims to address this problem. I should look at it more often. In 2009, there was a nice 50th-anniversary issue, featuring some significant articles, with retrospective commentary. For example, there is a fascinating article about Snow Crystals by F.C. Franks.

My UQ colleague, Ben Powell recently submitted a nice review to the journal.

Emergent particles and gauge fields in quantum matter 

I give a pedagogical introduction to some of the many particles and gauge fields that can emerge in correlated matter. The standard model of materials is built on Landau's foundational principles: adiabatic continuity and spontaneous symmetry breaking. These ideas lead to quasiparticles that inherit their quantum numbers from fundamental particles, Nambu-Goldstone bosons, the Anderson-Higgs mechanism, and topological defects in order parameters. I then describe the modern discovery of physics beyond the standard model. Here, quantum correlations (entanglement) and topology play key roles in defining the properties of matter. This can lead to fractionalised quasiparticles that carry only a fraction of the quantum numbers that define fundamental particles. These particles can have exotic properties: for example Majorana fermions are their own antiparticles, anyons have exchange statistics that are neither bosonic nor fermionic, and magnetic monopoles do not occur in the vacuum. Gauge fields emerge naturally in the description of highly correlated matter and can lead to gauge bosons. Relationships to the standard model of particle physics are discussed.

 

Kondo effect in the New York Times!

The Kondo effect is a paradigm for quantum many-body physics. It has so much: non-perturbative effects, scaling, emergent energy scales, Bethe ansatz solution, asymptotic freedom, Fermi liquid, ...

The Kondo model is a benchmark for testing many approximations and numerical methods.

Furthermore, it connects to so many other things: Anderson single impurity model, Dynamical Mean-Field Theory, Kosterlitz-Thouless transition, heavy fermions, ...

Nevertheless, outside the strongly correlated electron community, it is not widely known, and particularly not in popular discussions of science.

I never thought it would feature at the beginning of the New York Times article, unless Jun Kondo (now 90 years old) was awarded a belated Nobel Prize.

I was pleasantly surprised to see a long profile of Myriam Sarachik that began with her experimental work on the Kondo effect back in 1963.

The article also chronicles some of the sexism she faced in her career and the very limited employment options there were for women in physics. The article also describes how she was not very "productive" for a decade due to recovering from the personal tragedy of the murder of her daughter. Yet, as her mental health recovered she made significant contributions: quantum tunneling in single molecule magnets and the metal-insulator transition in semiconductor heterostructures.

There is a longer autobiographical piece in Annual Reviews.

Emergence, surprises, and the future of condensed matter physics

 Where is condensed matter physics heading? Does it have a bright future? What are the big questions the field aims to (and might actually) address? What might we predict?

I need to address these kinds of questions in the last chapter of Condensed Matter Physics: A Very Short Introduction.

Here are three different perspectives.

1. Incremental advances.

We will continue to make advances on many fronts: chemical synthesis, device fabrication, experimental techniques, theory, computation, intellectual synthesis, connections with other disciplines, and technological applications. The basic intellectual structure of the discipline is in place. In the framework of Thomas Kuhn, it is "normal science" and we don't expect any "paradigm shifts." John Horgan provocatively proclaimed a quarter of a century ago that it is The End of Science.

2. Hype.

All of the forthcoming incremental advances will combine together to produce a revolution: materials by design. Suppose we want a material with specific properties, e.g., room temperature superconductivity with a high critical current density, and processible into durable wires.... We put this information into the computer and it will tell us the chemical composition, synthesis method, crystal structure, and material properties.

3. We don't know. Expect big surprises as we explore the endless frontier.

Condensed matter physics is all about emergent phenomena. By definition, emergent phenomena are hard to predict, even when you know many (or all) of the details of the system components and their interactions. They are often surprising. Sometimes we can explain (or at least rationalise) them a posteriori (after the fact) by rarely a priori. 

Just consider some of the long list of exotica from the past four decades: quantum Hall effects, many new classes of superconductors (heavy fermion, organic, cuprate, iron-based, buckyballs, cobaltates, ..), non-Fermi liquid metals, topological insulators, graphene, twisted graphene, colossal magnetoresistance, spin ices, macroscopic quantum tunneling magnets, superconducting qubits, ... Note that almost all of these were experimental discoveries first. Theorists may have had some inklings and broad suggestions of what to look for and where. However, that is quite different from there being consensus and expectation. For example, compare and contrast these discoveries with the case of the experimental discovery of the Higgs boson. It really wasn't that surprising and there was a strong consensus among theorists; both that it would be there and what specific properties it would have.

Perhaps, serendipity remains the best method of discovery.

What's next? Who knows?!

All I am game to predict is that CMP will continue to be an exciting discipline with many surprises and intellectual challenges.

What do you think?

What's the big deal about twisted bilayer graphene?

 Twisted bilayer graphene seems to be the hottest topic in condensed matter physics right now. I tend to not follow fashion, both in clothing and science, for a multitude of reasons. However, I recently tried to catch up and read several of the nice perspectives on the topic at the Journal Club for Condensed Matter Physics.

Electronic bands of twisted graphene layers by Francisco Guinea

New correlated phenomena in magic-angle twisted bilayer graphene/s by Michael Zaletel.

What drives superconductivity in twisted bilayer graphene? by T. Senthil

Here are just a few big picture comments. I welcome feedback. I am just dipping into the subject.

Why is this attracting so much interest?

It is a playground for both experimentalists and theorists. There is some beautiful mathematics, even at the level of Moire patterns, large unit cells for the crystal structure (7204 carbon atoms!), and electronic band structure. For experimentalists, it presents a tuneable system with a rich phase diagram.

The band structure is unique in having topological features (Chern numbers), Wannier orbitals with subtle features, and non-abelian gauge fields.

The discovery of superconductivity and ferromagnetism was unexpected (I think).

There is a subtle competition between many different strongly correlated phases: Mott insulators, ferromagnetism, superconductivity, Dirac metals, ...

The possibility that superconductivity is associated with (i.e. in close proximity in the phase diagram) a Mott insulator suggests some possible similarities to cuprate superconductors.

What are some outstanding issues?

All the theory has a precise and uniform twist angle between the two sheets of graphene. However, there will inevitably be some spatial inhomogeneity in the twist angle across any real laboratory sample. How much does this inhomogeneity matter in the experiments that have been reported so far?

What is the role of the substrate that the twisted bilayer sits on?

Is the superconductivity always "derived" from a Mott insulator?

Is the superconductivity unconventional in being non-phononic and/or having non-s-wave pairing?

Can we achieve consensus on a model effective Hamiltonian and what its phase diagram is?

Will this interest last?

Interest may fade if further and more careful experiments on better samples can never definitely answer the questions above OR if the experiments do find some of the following to be true.

The sample inhomogeneity matters and some of the exciting results reported do not survive in better samples.

The superconductivity is not intimately connected to the Mott insulator.

The superconductivity is conventional.

Some caution and skepticism are in order. Many results published in luxury journals do not stand the test of time. Furthermore, condensed matter physics is a field that rapidly goes through fashions that attract a crowd that quickly moves onto to the next ``big thing,'' i.e. exotic phenomena.

I welcome comments and corrections. I do want to learn more about this fascinating subject.

The intellectual legacy of Phil Anderson

I am looking forward to reading Andrew Zangwill's book, A Mind Over Matter: Philip Anderson and the Physics of the Very Many, that should be available in January 2021.

Andy recently gave a beautiful talk at an ICAM meeting on the life and science of Phil Anderson. I highly recommend it. Yesterday, at the UQ condensed matter theory group meeting we watched it and discussed it.

A few things that stood out to me, partly because some were new to me.

``PWA was a brilliant intuitionist who did more than any other person to transform the patchwork of ideas and techniques of what was formerly called solid state physics into the deep, subtle, and intellectually coherent discipline know as condensed matter physics.''

Phil's wife, Joyce, had an MA in English literature and edited all his prose pieces. This may explain how well written his writing for general audiences, such as Physics Today columns and book reviews in The Times Higher Education Supplement were so well written. In contrast, Phils talks and some papers were rather obscure.

PWA was a contrarian. He did not follow the pack. This is embodied in the fact that he chose to work on his PhD at Harvard with van Vleck, rather than Schwinger, who was chosen by eleven of his peers! van Vleck said "follow the data". During this time he was a friend of Tom Lehrer, a mathematics graduate student who became famous for writing and performing satirical songs with a strong social justice theme.

Phil did a BS in Electronic Physics (essentially Radio Engineering) and did not learn any modern physics. He did a PhD in chemical physics. It was only at Bell Labs that he started working on condensed matter problems. There he had three significant mentors: Conyers Herring, Gregory Wannier, and Charles Kittel.

Phil's 1952 paper on antiferromagnetism contained the idea of spontaneous symmetry breaking. But, this was not appreciated for a decade.

Phil's 1957 localisation paper and his 1961 magnetic impurities paper [the two works cited for his Nobel Prize] were both stimulated by talking to experimentalists at Bell Labs [George Feher and Berndt Matthias, respectively].

Concepts in Solids, based on his graduate lectures at Cambridge in 1961-2, was revolutionary for the time because the focus was on the properties of model Hamiltonians, rather than detailed phenomenology.

Phil's criticisms of high energy physics, its reductionism and drawing resources away from "tabletop" science, began as early as 1971, when he wrote a New Scientist article on the subject. 

But there is a lot more. Watch the video!

Condensed matter physics is not axiomatic

 When I was an undergraduate I loved taking courses in pure mathematics and physics. I never took the "Solid State Physics" course because the person who taught it was a hopeless teacher. In my honours year (final year) I wrote a thesis on "Gravitational Lenses" that involved proving some theorems in General Relativity. I wanted to do a PhD in mathematical physics, which is why I chose to take an offer from Princeton rather than Cornell. Nevertheless, I am very glad I ended up doing condensed matter.

I only just realised that there is a basic and fundamental thing about condensed matter that distinguishes it from all the physics courses I took and loved as an undergraduate. In simple and loose terms, CMP is not axiomatic. I don't meet this in a rigorous mathematical sense, but rather the following. Consider classical mechanics, thermodynamics, statistical mechanics, electromagnetism, special relativity, general relativity, and quantum mechanics. For all of them, particularly at the undergraduate level, you can write down just a few equations  (or laws) and everything else follows. It can almost become an exercise in applied mathematics. At least that is how I viewed it. This is why undergraduate physics can be quite easy for nerds who are good at calculus and linear algebra. 

On the positive side, this "axiomatic" character to these physics subjects is rather beautiful because of the simplicity of the fundamental laws/equation. Furthermore, in some cases, one can argue that one subject can be largely summarised in a single variational principle, such as the extrema of the action.

In contrast, CMP really does not have comparable "axioms" or laws. All it has are certain organising principles such as spontaneous symmetry breaking, emergence, quasi-particles, topological order, ...

Perhaps, I mean CMP is not reductionist or "fundamental", rather than not axiomatic. 

CMP is hard for undergraduates because it involves drawing together practically everything they have learnt: mechanics, electromagnetism, quantum, statistical mechanics, thermodynamics, .. 

This lack of an axiomatic character may be a second reason why CMP is hard for undergraduates, particularly for those like me who have found other physics subjects "easy".

What do you think?