The dirt on spin liquids

The organic charge transfer salt -(ET)₂Cu₂(CN)₃ has attracted a lot of attention the past few years because there is significant experimental evidence that the ground state of the Mott insulating phase is a spin liquid.

One important and puzzling observation is that the NMR lines are much more broadened than those of comparable materials undergo antiferromagnetic ordering. Furthermore, this broadening increases significantly with decreasing temperature.

A nice paper by Gregor and Motrunich performs several model calculations to see if they can explain this large broadening by taking into account the role of disorder. They find they can only explain the experimental data above about 5 K, if there is much larger disorder than expected and that it is strongly temperature dependent.

It is interesting that the authors have done comparable calculations for a kagome antiferromagnetic and they can explain the experimental data for that.

Gregor and Motrunich mention that it is hard to estimate the strength of the disorder and the role of temperature dependent screening.

A recent paper by two of my UQ colleagues may help a:

Toward the parametrization of the Hubbard model for salts of bis(ethylenedithio)tetrathiafulvalene: A density functional study of isolated molecules

J. Chem. Phys. 130, 104508 (2009)

http://link.aip.org/link/?JCPSA6/130/104508/1

They find that the difference in the site energies for BEDT-TTF molecules in the staggered and eclipsed conformations is 0.12 eV.

I note that this is comparable to the single dimer Hubbard U ~ 0.2 eV estimated from the optical conductivity. This could have a big effect on the exchange interaction between the localised spins in the Mott insulating phase (see equation B2 in Gregor & Motrunich).

Hopefully, the findings in these two papers can be combined to pin down just how large the disorder is in this material, which is such a promising candidate for a spin liquid.

The two really hard questions that remain are:

Is the large line broadening a definitive signature of a gapless spin liquid?

Is disorder essential to understand this line broadening?

Increasing our scientific productivity (but writing less papers)

There is a article in Science that I have now read three times and am wrestling with. I reproduce a few quotations below:

Strong inference consists of applying the following steps to every problem in science, formally and explicitly and regularly:

1) Devising alternative hypotheses;
2) Devising a crucial experiment (or several of them), with alternative possible outcomes, each of which will, as nearly as possible, exclude one or more of the hypotheses;
3) Carrying out the experiment so as to get a clean result;
1') recycling the procedure, making subhypotheses or sequential hypotheses to refine the possibilities that remain; and so on.
......
"But what is so novel about this?" someone will say. This is the the method of science and always has been; why give it a special name? The reason is that many of us have almost forgotten it. Science is now an everyday business. Equipment, calculations, lectures, become ends in themselves. ... we do busywork. We become "method-oriented" rather than "problem" oriented. .. We fail to teach our students how to sharpen up their inductive inferences.
.....
Whether it is hand-waving or number-waving or equation-waving, a theory is not a theory unless it can be disproved.

[but a single hypothesis is difficult to disprove. Furthermore,]
"our trouble is that when we make a single hypothesis, we become attached to it"

[this is why] some great scientists are so disputatious

To avoid this grave danger [of people being attached to theories], the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections.

[Examples are given from Faraday, Roentgen, Fermi, Watson & Crick, and Pasteur]
these men believed in the effectiveness of daily steps in applying formal inductive methods to one problem after another

[we should all] devote a half hour or an hour to analytical thinking every day, writing out the logical tree and the alternatives and crucial experiments explicitly in a permanent notebook.

The article is by John R. Platt, a distinguished molecular spectroscopist from the University of Chicago. It was published in 1965, but seems just as relevant and important today!

I welcome comments, and especially examples of multiple hypotheses.

A further twist on optically active molecules

Understanding the quantum dynamics of the excited states of complex molecular materials is a scientific challenge that is of great technological importance.
From a physics point of view we would like to know which details really do matter in determining functionalities such as the light induced charge separation required in solar cells.

Methine dyes are an important class of materials for organic photonics.
Previously I discussed how Seth Olsen and I published a paper

A diabatic three-state representation of photoisomerization in the green fluorescent protein chromophore

J. Chem. Phys. 130, 184302 (2009)

http://link.aip.org/link/?JCPSA6/130/184302/1

We have also done a very detailed study of the topology and geometry of the potential energy surfaces for the low-lying singlet states for an effective Hamiltonian describing the three valence bond states relevant to methine dyes.

Important degrees of freedom are the different twists shown below.
Even this simple model exhibits much of the rich geometry and several key properties found previously in very sophisticated quantum chemistry calculations: the existence of conical intersections between different states and charge localisation connected with excited state twisting. Just one case is shown below.

Philosophers wrestle with emergence

The concept of emergence has received significant attention in philosophical circles, from early in the twentieth century. Here, it is important to make the distinction between "weak" emergence and "strong" emergence. Philosophers such as Broad and Alexander were advocates of what would be now called "strong" emergence. A position of strong emergence holds that emergent properties cannot, even in principle, be deduced from the properties of the constituents of the system. Vitalism, the notion that living matter, is not purely physical, is an example of such a view.

A reductionist would claim we can always understand all the properties of a complex system in terms of the properties of its constituent particles and their interactions. Given sufficient computational resources we can predict properties of the whole system. In contrast, someone advocating "weak" emergence acknowledges it may be possible "in principle" to deduce emergent properties from properties of the constituents of the system. However, they would emphasize that in practice (at least, at this point in time) we cannot make such deductions. Furthermore, such deductions do not necessarily provide significant insight or allow one to deduce the organizing principles of the system under study.

Sometimes a "strong" emergence position is associated with "top-down causation" or "downward causation", in contrast to the notion of "bottom-up causation" which a reductionist advocates.

Silberstein and McGeever discuss how the distinction between "weak" and "strong" emergence can also be viewed as a distinction between epistemological emergence and ontological emergence:

A property of an object or system is epistemologically emergent if the property is reducible to or determined by the intrinsic properties of the ultimate constitutents of the object or system, while at the same time it is very difficult for us to explain, predict or derive the property on the basis of the ultimate constituents.

Ontologically emergent features are neither reducible to nor determined by more basic features. Ontologically emergent features are features of systems or wholes that possess causal capacities not reducible to any of the intrinsic causal capacities of the parts nor to any of the (reducible) relations between the parts.

They claim that the existence of entangled states in quantum mechanics provides the most conclusive evidence for the existence of ontological emergence and that this completely explodes the ontological picture of reality as divided into a `discrete hierarchy of levels’ and they quote Humphreys statement ,

even if the ordering on the complexity of structures ranging from those of elementary physics to those of astrophysics and neurophysiology is discrete, the interactions between such structures will be so entangled that any separation into levels will be quite arbitrary

However, this argument overlooks the fact that entangled quantum states are very fragile and their interaction with the environment can quickly "decohere" them and destroy the entanglement. This is how classical mechanics emerges from quantum mechanics. It is possible to show that in biomolecules this decoherence occurs in less than a picosecond, which is why large scale quantum entanglement does not play a role in biochemical phenomena.

In considering the relationship between chemistry and physics, Lombardi and Labarca reject the separation of ontological and epistemological emergence. They work within the framework of Hilary Putnam’s internal realism, which aims to find middle ground between metaphysical realism and radical relativism. Conceptual schemes and descriptions are required to define objects, even though reality exists independent of our subjective description.

Getting the elephant's trunk to wiggle

The Nature essay, A meeting with Enrico Fermi, by Freeman Dyson is worth digesting. I quote below a few bits that stood out to me:

I am eternally grateful to him for destroying our illusions and telling us the bitter truth.

we could calculate the atomic processes precisely. By 1951, we had triumphantly finished the atomic calculations and were looking for fresh fields to conquer. We decided to use the same techniques of calculation to explore the strong nuclear forces.

[Fermi said:]
"There are two ways of doing calculations in theoretical physics", he said. "One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither...
....To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics....
....my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

Orbitals that do exist

Previously I discussed why I don't like the way some people talk about LUMO's and HOMO's. They don't really exist, i.e., they have no measurable properties.
They are very useful for qualitative discussions though.

Is there something better, that respects the fact that the ground state of molecules is really
a highly correlated quantum many-body state?

Yes. Natural orbitals. These are the eigenfunctions of the full one-particle density matrix.
The corresponding eigenvalues are the occupation of these orbitals.
Note these can have non-integer values.
There is a connection to Fermi liquid theory, which I hope to come back to....

A nice introduction can be found in
Sections 1.5 & 1.6 of the wonderful book, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective, by Frank Weinhold and Clark Landis.
The book shows how to ground chemical intuition (orbitals, lewis pairs, bonding) in a rigorous theoretical framework.

The excitement of when theory meets experiment

I was delighted to see that Jukka Pekola is going to be at UQ on friday to give the physics colloquium. He is a very gifted experimentalist. i.e., he can do many experiments that other people can't get to work.

I first met Jukka (hard to believe!) 20 years ago. I had just completed a Ph.D with the onerous title, "Nonlinear interaction of zero sound with order parameter collective models in superfluid 3He-B."
This explored various acoustic analogues of non-linear optical effects.

I gave a talk on this work at a conference in Florida and later we went to lunch and Jukka said, "we tried to do the experiment you proposed and it did not work." I was delighted that someone had tried! The proposed experiment was to observe two-phonon absorption by the real squashing mode (one of the 18 order parameter collective modes in 3He-B). This required keeping the superfluid at a constant and uniform millikelvin temperature while dumping large amounts of energy into it to produce large amplitude density oscillations. A very difficult experiment....

Jukka's group had tried the experiment at high pressures. I suggested to Jukka that the effect may be more observable at lower pressures because the non-linear coupling would be larger due to the pressure dependence of a relevant Landau Fermi liquid parameter.

Jukka went back to Helsinki and successfully did the experiment! This was exciting for me. We wrote a paper together describing the results. Later we realised this non-linear effect could be used to map out the dispersion relation for the squashing mode (described in this PRL). I was also invited to a conference in Helsinki and I got to see the lab where it all happened! ( see the photos). I gave an overview/summary of all the work in my conference paper.

This was the first of many fruitful collaborations I have now had with experimentalists. Thanks are due to Jukka for getting me started. I look forward to catching up with him on friday.