Mental health talk in Canberra

Today I am giving a talk to scientists [mostly postdocs and grad students] at the Black Mountain laboratories of CSIRO [Australia's national industrial labs].
Here are the slides.

On the personal side there is something "strange" about the location of this talk. It is less than one kilometre from where I grew up and was an undergrad. Back then I never even thought about these issues.

Another bad metal talk

Today I am giving a talk on bad metals at the 2013 Gordon Godfrey Workshop on Strong Electron Correlations and Spins in Sydney.
Here is the current version of the slides for the talk.

One question I keep getting asked is, "Are these dirty systems?" NO! They are very clean. The bad metal arises purely from electron-electron interactions.

The main results in the talk are in a recent PRL, written with Jure Kokalj.

The organic charge transfer salts and the relevant Hubbard model are discussed extensively in a review, written with Ben Powell. However, I stress that this bad metal physics is present in a wide range of strongly correlated electron materials. The organics just provide a nice tuneable system to study.
A recent review of the Finite Temperature Lanczos Method is by Peter Prelovsek and Janez Bonca.

The emergence of "sloppy" science

Here "sloppy" science is good science!

How do effective theories emerge?
What is the minimum number of variables and parameters needed to describe some emergent phenomena?
Is there a "blind"/"automated" procedure for determining what the relevant variables and parameters are?

There is an interesting paper in Science
Parameter Space Compression Underlies Emergent Theories and Predictive Models
Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna

These issues are not just relevant in physics, but also in systems biology. The authors state:

important predictions largely depend only on a few “stiff” combinations of parameters, followed by a sequence of geometrically less important “sloppy” ones... This recurring characteristic, termed “sloppiness,” naturally arises in models describing collective data (not chosen to probe individual system components) and has implications similar to those of the renormalization group (RG) and continuum limit methods of statistical physics. Both physics and sloppy models show weak dependence of macroscopic observables on microscopic details and allow effective descriptions with reduced dimensionality.

The following idea is central to the paper.

The sensitivity of model predictions to changes in parameters is quantified by the Fisher Information Matrix (FIM). The FIM forms a metric on parameter space that measures the distinguishability between a model with parameters theta_m and a nearby model with parameters theta_m + delta theta_m.

The authors show that for several specific models, the eigenvalue spectrum of the FIM is dominated by just a few eigenvalues. These eigenvalues are then associated with the key parameters of the theory.

I have one minor quibble with the first sentence of the paper.

"Physics owes its success (1) in large part to the hierarchical character of scientific theories (2)."

Reference (1) is Eugene Wigner's famous 1960 essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
Reference (2) is Anderson's classic "More is different".

I think Wigner's paper is largely about something quite different from emergence, the focus of Anderson's paper. Wigner is primarily concerned with the even more profound philosophical question as to why nature can be described by mathematics at all. I see no scientific answer on the horizon.

Update. The authors also have longer papers on the same subject

Perspective: Sloppiness and emergent theories in physics, biology, and beyond 

Mark K. Transtrum; Benjamin B. Machta; Kevin S. Brown; Bryan C. Daniels; Christopher R. Myers; James P. Sethna 

(2015)

Review: Information geometry for multiparameter models: new perspectives on the origin of simplicity

Katherine N Quinn, Michael C Abbott, Mark K Transtrum, Benjamin B Machta and James P Sethna

(2022)

The commuting problem

I am not talking about commuting operators in quantum mechanics.

When considering a job offer, or the relative merits of multiple job offers [a luxury] rarely does one hear discussion of the daily commute associated with the job. Consider the following two options.

A. The prestigious institution is in a large city and due to the high cost of housing you will have to commute for greater than an hour. Furthermore, this commute involves driving in heavy traffic or taking and waiting for crowded public transport.

B. A less prestigious institution offers you on campus [or near campus] housing so you can walk 5-15 minutes to work each day.

The difference is considerable. Option A will waste more than 10 hours of each week and increase your stress and reduce your energy. In light of that you may end up being more productive and successful at B.

It is interesting that

I realise the options often aren't that simple. Furthermore, you may not have a choice. Also, time is not the only factor. A one hour train ride to and from work each day may not be that bad if you can always get a seat and there are tables to work on. Some people really enjoy a 40 minute bicycle ride to and from work each day.

I am just saying it is an issue to consider.

I once had an attractive job offer that I once turned down largely because of commuting . I am glad I did. So is my family.

Bad metal talk at IISc Bangalore

Today I am giving a seminar in the Physics Department at the Indian Institute of Science in Bangalore.
Here is the current version of the slides.

The main results in the talk are in a recent PRL, written with Jure Kokalj.

The organic charge transfer salts and the relevant Hubbard model are discussed extensively in a review, written with Ben Powell.

The role of universities in nation building

There is a general view that great nations have great universities. This motivates significant public and private investment [both financial and political] in universities.
Unfortunately, these days much of the focus is on universities promoting economic growth.
However, I think equally important are the contributions that universities can make to culture, political stability, and positive social change.

Aside: Much of this discussion assumes a causality: strong universities produce strong nations. However, I think caution is in order here. Sometimes it may be correlation not causality. For example, wealthy nations use their wealth to build excellent universities.

The main purpose of this post is to make two bold claims. For neither claim do I have empirical evidence. But, I think they are worth discussing.

First some nomenclature. In every country the quality of institutions decays with ranking. In different countries that decay rate is different. Roughly the rate decreases from India to Australia to the USA. Below I will distinguish between tier 1 and tier 2 institutions. It is not clear how to define the exact boundary. But, roughly the number of tier 1 would be no more than 50, 10, and 10 for  the USA, India, and Australia respectively. Let's not get in a big debate about how big this number is.

So here are the claims.

1. The key institutions for nation building are not the best institutions but the second tier ones.

2. Making second tier institutions effective is much more challenging than first tier institutions.

Let me try and justify each claim.

1. Great nations are not just build by brilliant scientists, writers and entrepreneurs.
Rather they also require effective school teachers, engineers, small business owners,...
Furthermore, you need citizens who are well informed, critical thinkers and engaged in politics and communities. The best universities are populated with highly gifted and motivated faculty and students. Most would be productive and successful, regardless of fancy buildings or high salaries. The best students will learn a lot regardless of the quality of the teaching. You don't need to teach them how to write an essay or to think critically. In contrast, faculty and students at second tier institutions require significantly more nurturing and development.

2.  At tier one institutions governments [or private trustees] just need to provide a certain minimal amount of resources and get out of the way. However, tier two institutions are a completely different ball game. Many are characterised by form without substance.
To be concrete, you can write impressive course profiles, assign leading texts, give lectures, and have fancy graduation ceremonies, but at the end students actually learn little. This painful reality is covered up by soft exams and grading. The focus in on rote learning rather than critical thinking.
Faculty may do research in the sense that they get grants, graduate Ph.D students, and publish papers.
However, the "research" and the Ph.D graduates are of such low quality they make little contribution to the nation.
The problem is accentuated by the fact they many of these institutions don't want to face the painful reality of the low quality of their incoming students and so they don't adjust their mission and programs accordingly. They just try to mimic tier one institutions.
Reforming these institutions is particularly difficult because they are largely controlled by career administrators who have no real experience or interest in real scholarship or teaching. Instead, they are obsessed with rankings, metrics, reorganisations, buildings, money, and particularly their own careers.

I think these concerns are just as applicable to countries as diverse as the USA, Australia, and India.
For a perspective on the latter, there is an interesting paper by Sabyasachi Bhattacharya
Indian Science Today: An Indigenously Crafted Crisis He was  a recent director of the Tata Institute for Fundamental Research.
I also found helpful a Physics World essay by  Shiraz Minwalla.

I welcome comments.

The challenge of intermediate coupling

The point here is a basic one. But, it is important to keep in mind.

One might tend to think that in quantum many-body theory the hardest problems are strong coupling ones. Let g denote some dimensionless coupling constant where g=0 corresponds to non-interacting particles. Obviously for large g perturbation theory is most unreliable and progress will be difficult. However, in some problems one can treat 1/g as a perturbative parameter and make progress. But this does require the infinite coupling limit be tractable.

Here are a few examples where strong coupling is actually tractable [but certainly non-trivial]

• The Hubbard model at half filling. For U much larger than t, the ground state is a Mott insulator. There is a charge gap and the low-lying excitations are spin excitations that are described by an antiferromagnetic Heisenberg model. Except for the case of frustration, i.e. on a non-bipartite lattice, the system is well understood.
• BEC-BCS crossover in ultracold fermionic atoms, near the unitarity limit.
• The Kondo problem at low temperatures. The system is a Fermi liquid, corresponding to the strong-coupling fixed point of the Kondo model.
• The fractional quantum Hall effect.

But, many of the problems of greatest interest are in an intermediate coupling region.

• Cuprate superconductors. For a long time it was considered that they are in the large U/t limit [i.e. strongly correlated] and that the Mottness was essential. However, Andy Millis and collaborators argue otherwise, as described here. It is interesting that one gets d-wave superconductivity both from a weak-coupling RG approach and a strong coupling RVB theory.
• Quantum chemistry. Weak coupling corresponds to molecular orbital theory. Strong coupling corresponds to valence bond theory. Real molecules are somewhere in the middle. This is the origin of the great debate about the relative merits of these approaches.
• Superconducting organic charge transfer salts. Many can be described by a Hubbard model on the anisotropic triangular lattice at half filling. Superconductivity occurs in proximity to the Mott transition which occurs for U ~ 8t. Ring exchange terms in the Heisenberg model may be important for understanding spin liquid phases.
• Graphene. It has U ~ bandwidth and long range Coulomb interactions. Perturb it and you could end up with an insulator.
• Exciton transport in photosynthetic systems. The kinetic energy, thermal energy, solvent reorganisation energy, and relaxation frequency [cut-off frequency of the bath] are all comparable.
• Water. This is my intuition but I find it hard to justify. It is not clear to me what the "coupling constants" are.

Aside from "brute force" numerical methods one is forced to attack these problems from either the weak-coupling or strong-coupling sides, hoping that one is capturing the essential physics. Sometimes one can come up with clever approximations that capture both the weak and strong coupling limits, and one hopes interpolates between the two. An example is Iterative Perturbation Theory used as an "impurity solver" in Dynamical Mean-Field Theory (DMFT). But, the big question arises whether there are intermediate coupling fixed points / phase transitions.

Intermediate coupling is both a blessing and a curse. It is a blessing because there is lots of interesting physics and chemistry associated with it. It is a curse because it is so hard to make reliable progress.

I welcome suggestions of other examples.