Slow/good/fun science

Ben Powell alerted me to a stimulating post and comments about "Slow science" on the Quantum Pontiff blog.

It is worth thinking about. Here are a few random thoughts:

This gets back to a point I made in a few earlier "career advice" posts. Good reliable influential science is hard. Consequently, it is slow.

I think we all need to do more "slow" science. We would produce higher quality work AND enjoy ourselves more.

Don't blame the "system".
Focus on your "circle of influence" (e.g, what you CAN change: how you choose to spend your time, how you review grant proposals, and papers) rather than your "circle of concern" (i.e., what you care about but can't change, e.g., the way universities hire, promote, etc., funding agencies make decisions).

In spite of all the flaws of the "system" and the bean counters I think it is still clear that really significant work is rewarded.

I agree with John Preskill (and Clint Eastwood) each of us need to know our limitations. We are not all as brilliant as some of those who practice "slow" science, produce significant work, and prosper. We need to distinguish cause and effect. Trying to emulate Kitaev, Duncan Haldane, or John Cardy, Feynman, or Lars Onsager is not an option for most of us!

Tobias Osborne asks where does the pressure come from to keep producing papers ("correct but boring") and be in the limelight?
I think it is largely internal, i.e., psychological.
It is from habit, addiction, desire for affirmation,..
It is easier than the hard work of doing significant work.

Would you like to be freed up to spend 20% of your time doing "slow" science?
Here's how. It is "simple". Just say NO to 20% of the requests you get to collaborate, write conference papers, apply for grants, give seminars, review papers, review grants, sit on committees, go to conferences, .....
I doubt that the resulting 20% cut in "productivity" (hopefully, the 20% least valuable) will have much impact on how impressive your CV is.

The naked truth versus self-deception

“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. ”

John von Neumann (via Enrico Fermi and Freeman Dyson)

I believe that any significant physical effect/discovery should be able to be seen by the naked eye in the experimental (or computational) data and should not require curve fitting.

For a helpful discussion, see Dangerous Curves.

The first principle is that you must not fool yourself--and you are the easiest person to fool

Richard Feynman, Caltech 1974 Commencement address

Emergence matters

Reality is stratified and science is hierarchial: from physics to chemistry to biochemistry to biology to psychology. Generally, as one goes up the strata the complexity of the system under study increases and the relevant length and time scales become greater. At each strata or level of hierarchy, science seeks to illuminate what are the principles that describe the phenomena under study. Sometimes principles can be reduced to and understood in terms of principles from the strata below. For example, genetics can be understood in terms of molecular biology. Rules of chemical bonding can be understood in terms of quantum physics. However, it should be stressed that there are very few specific cases where phenomena at one strata have been predicted solely from a knowledge of the laws underlying strata below. In almost all cases, one observes (n.b., not deduces) phenomena at one level, develops concepts to understand them at that level, and then a posteriori tries to understand them in terms of the laws from the level below.

Perhaps is not appreciated enough just how hard it is to predict properties of quantum many-body systems. New phases of matter continue to be discovered: liquid crystals, quasicrystals, antiferromagnets, superfluids, …. Yet I am only aware of one case where a new state of matter was predicted and then discovered; that is Bose-Einstein condensates in dilute atomic gases were predicted.

Quantum chemistry involves using Schrodinger’s equation to calculate properties of molecules. It has many successes at calculating observed properties of small molecules. However, a measure of its limitations is the citation that one of the world leaders in the field, Fritz Schaefer, received for award of the Centenary Medal of the Royal Society of Chemistry in 1992: ``the first theoretical chemist successfully to challenge the accepted conclusions of a distinguished experimental group for a polyatomic molecule, namely methylene.”


In his classic More is Different paper, Phil Anderson emphasised that the success of methodological micro-reductionism does not imply a constructivist hypothesis: if we know the laws of one strata we can deduce the laws of the next strata above. Since making predictions from one strata to the next is so difficult, if not impossible, an a posteriori approach rather than an a priori approach is often necessary.

Closing the gaps in our understanding

As we struggle to understand the pseudogap state in the cuprate superconductors any successful theory must be able to describe at least qualitatively a few key features:

• the d-wave symmetry
• the existence of Fermi arcs which increase in length with doping
• well-defined quasi-particles near the nodes
  
• incoherent excitations near the anti-nodes

Can a one-band Hubbard model capture such features?

Furthermore, if it can, is there a "simple" physical picture of the underlying physics?

I believe that affirmative answers to both questions are given in a very nice preprint by Ferrero, Cornaglia, De Leo, Parcollet, Kotliar, and Georges.

Some of the results were published earlier in PRL, which contains the nice figure below of
the spectral function at the chemical potential at different doping away from half filling.

This work builds on the successes of Kotliar and Georges at developing Cluster Dynamical Mean-Field Theory (DMFT), rotationally invariant slave boson theory, and orbital-selective Mott transitions.

They divide momentum space into just two regions and consider the associated two-site DMFT. Symmetric and anti-symmetric combinations of the two sites correspond to the nodal and anti-nodal regions, respectively.
Formation of the pseudogap is associated with a Mott transition in the anti-symmetric orbital. The different behaviours of the two orbitals (momentum regions) is due to the formation of inter-site spin singlets. They compare the essential physics to that which occurs in the two-impurity Anderson model. In that case there is competition when formation of a singlet between the two impurities and two separate Kondo singlets between
each of the impurity spins and the itinerant electrons.

The calculations agree well with STM and ARPES experiments.

Abolish conference proceedings!

I almost never take up an offer by conference organisers
to publish a paper in their proceedings. I think such
proceedings have passed their use by date because:

* They usually appear 6 to 18 months after the conference.
By then most of the papers have already been published elsewhere

* Almost all conference papers seem to be cut-and-paste versions
of papers that the authors have already published or about to
publish elsewhere.

* Most proceedings are published by mediocre journals.

* One of the main reasons some people publish in them is to pad their
publication lists and keep bean counters happy.

* The only conference papers I tend to read are review articles based on plenary talks by leading scientists. But, most of these I get off the arXiv.

Given all of the above I think conference proceedings are just a
waste of time for the organisers, referees, and authors.
We should all exercise more self-control and abstain.

What is reductionism?

In order to understand the role and implications of emergence it is helpful to define different forms of reductionism in science. It is also important to make a distinction between reductionism as a practice in science and reductionism as a philosophical outlook. As a method, reductionism has been extremely powerful. Examples of successes include the understanding obtained by reducing genetics to molecular biology, atomic spectra to quantum mechanics, and planetary motion to Newtonian mechanics. A reductionist approach gave a unifying description of a diverse range of phenomena, and elucidated "cause and effect", i.e., if one component or variable of the system is changed what is the resulting change in other components or properties. In terms of popular books, advocates of the primacy of reductionism include Steven Weinberg, Stephen Hawking, and Richard Dawkins. They also appear to presuppose that because reductionism is a fruitful strategy for certain scientific problems that these means that a philosophical reductionism must be universally valid.

The Oxford Companion to Philosophy considers three aspects of philosophical reductionism: ontological, methodological, and theory.

Ontological reductionism "refers to the belief that the whole of reality consists of a minimal number of entities." For example, humans are really just self-organising biochemical systems or that the world is just a collections of quarks, leptons, and gauge fields. This often appears to involve value judgements as to what is "real" and what is not.

Methodological reductionism claims that ``the best scientific strategy is always to attempt explanation in terms of ever more minute entities.’’ One can differentiate this methodology further in terms of micro-reductionism and macro-reductionism. The former focuses on explaining phenomena at one strata in terms of the next lowest level strata. For example, genetics can be understood in terms of DNA. Macro-reductionism goes much further, claiming to explain phenomena at one level in terms of phenomena at a much lower strata. Socio-biology is an example of macro-reductionism. Micro-reductionism has proven to be an extremely successful and fruitful strategy; it has led to a simplification of ideas and unification of knowledge. However, it is contentious whether it is always the best scientific strategy. Although macro-reductionism has prominent, articulate, and passionate advocates I am unable to think of any specific cases where it has actually been able to produce knowledge that has been accepted by a majority of scientists in the associated field.

Theory (or epistemological) reduction considers how one theory which replaces a prior one reduces to it in an appropriate limit. For example, Einstein’s theory of special relativity reduces to classical Newtonian mechanics in the limit of objects moving much less than the speed of light. Similarily, the equations of quantum physics reduce to those of classical mechanics in the limit of large objects. This was advocated by the ``Unity of science’’ movement in the 1930’s and the influential work by Nagel [The Structure of Science, (Harcourt, New York, 1961)] who claimed that reduced theories were just logical consequences of the reducing theory. Thomas Kuhn, considers that theory reduction is not possible because new theories often involve concepts and modes of explanation that are ``incommensurate’’ with prior theories. For example, although in appropriate mathematical limits quantum theory reduces to classical mechanics, they do not agree on whether on can ascribe a definite position and momentum to a single particle. A less radical view emphasizes the complexity and subtleties associated with theory reduction because it requires limiting procedures, coarse graining and approximations. [R. Batterman, The Devil in the Details. Asymptotic Reasoning in Explanation, Reduction, and Emergence (Oxford: Oxford University Press, 2002).]

Desperately seeking spin liquids

What is a spin liquid? There are several alternative definitions.
The definition that I think is the most illuminating, because it brings out their truely exotic nature, is the following. A spin liquid is a quantum state in which there is no long-range magnetic order and no breaking of spatial symmetries (rotation or translation).
One can write down many such states. A concrete example is the ground state of the one-dimensional antiferromagnetic Heisenberg model with nearest-neighbour interactions.
However, despite an exhaustive search since Anderson's 1987 RVB paper, it seems extremely difficult to find a physically realistic Hamiltonian in two dimensions which has such a ground state.

As far as I am aware we are still seeking a counter-example to the following conjecture:

Consider an spin-1/2 Heisenberg model on a two-dimensional lattice with short range antiferromagnetic exchange (both pairwise and ring exchange are allowed) interactions. The Hamiltonian is invariant under SU(2)xL, where L is a space group. Then the ground state spontaneously breaks at least one of the two symmetries SU(2) and L.

Or did I miss something?