Desperately seeking spin liquids, again

Previously I posted about recent numerical work which suggested that the Hubbard model on the honeycomb lattice and the Heisenberg model on the kagome lattice may have spin liquid ground states. At the Journal Club for Condensed Matter Physics, Steve Kivelson has a nice commentary on these two papers. One point important question he focuses on is whether or not these states have topological order, signified by a degenerate ground state, whose degeneracy only depends on the topology of the lattice [e.g. a torus].

Do biologists and physicists need each other?

Do biologists really need physicists and mathematicians? Will the need increase in the next few decades? What are the landmark contributions of quantitative methods to biology? Seth Olsen brought to my attention an article, Mathematics is Biology's Next Microscope, Only Better; Biology is Mathematics Next Physics, Only Better by Joel E. Cohen.
It is worth reading, especially because it has lists of

• Mathematics arising from Biological Problems [Important historical contributions]
• 5 Biological challenges that could stimulate, and benefit from, major innovations in mathematics
• 5 Mathematical challenges that would contribute to the progress of Biology
• Important references.

Here are a few random comments.

I am not sure I agree with the title. I would say the point is more:

Quantitative methods are Biology's next microscope.

Biological physics is the next playground for emergent concepts and model.

Quantitative biology may lead to some interesting new applied mathematics.

It is a worry that the vast majority of the list of mathematical contributions to biological problems involves contributions from more than 50 years ago. 

 

Back up now!

The recent floods in Brisbane highlighted to me how we always need to be prepared for low probability-high impact events. So I went out and bought a second hard drive for backup. I realised that having a laptop and backup in the same location is not sufficient. Fires, floods, and theft do happen. So don't just back up now. Get a second one in a different location. Furthermore, the earlier you are in your career the more important this is. Losing your thesis or all your data is the worst thing that can happen.

Towards the spin Bose metal

As discussed in earlier posts and this review a strong candidate two-dimensional quantum spin model to have a spin liquid ground state is the Heisenberg model on the anisotropic triangular lattice with some ring exchange K. This model is directly relevant to the Mott insulating state of various charge transfer salts.

Studying such frustrated two-dimensional models numerically is a major challenge, and getting definitive results is currently not possible [see e.g. my post about recent work on the Kagome lattice model]. In contrast in one dimension the  density matrix renormalisation group (DMRG) gives definitive results. Hence, one strategy is then to look at coupled chains in the hope that they capture essential physics.

There is a nice preprint by Block, Sheng, Motrunich, and Fisher which looks at the problem on a four chain system using the density matrix renormalisation group (DMRG). They find that once the ring exchange interaction K is larger than J/5 [quite a physically realistic value] that the ground state is a spin liquid: the spin Bose metal (SBM) proposed by Motrunich. They also studied the effect of spatial anisotropy and produced the   phase diagram below.

It is fascinating that the organic charge transfer salts have parameter values that are approximately in the region where all three different phases can occur.

I thank H.-H Lai for bringing this preprint to my attention.

A physicists view of hydrogen bonding

This afternoon I gave a talk at the cake meeting, "Empirical valence bond models for hydrogen bonding and proton transfer". The notes are here.

The figure below taken from a Chemical Reviews is interesting. It shows how for a 

O...H-O system the correlation been O-H bond length and the O..H bond length has a natural explanation in terms of bond order conservation. To me this shows that hydrogen bonds are essentially a resonance between a covalent bond and a charge transfer excitation, as proposed by Coulson.  i.e. the wavefunction is a superposition of  A-H... B and A-...+H-B. 

I need to write more negative posts!

My New Years wish for this blog is that it would attract more comments online. It now has several hundred pageviews per day, but rarely generates much discussion; except when it is occasionally provocative. It turns out there is some science to this. Read below a post Negatives attract  from another blogger

while doing some research for a piece in an upcoming Nature Chemistry column on the roll of blogging in chemistry (due out in March), I ran across a fascinating paper in the European Physical Journal B: "Networks and emotion-driven user communities at popular blogs." The authors mathematically analyzed the topology (connectedness) of a large network of blogs and posts, assessing the emotional content along the way. (If the word bipartite doesn't scare you, read the paper.) They noted that large communities grow around posts with very negative language - and in the absence of such posts, there ends up being far less "cross-talk" between blogs. Nasty posts acted as glue.

Their data suggests that being negative also makes you popular in the blog world. More negatively worded posts attract more comments. Negative language in the comments attract more comments. Being obnoxious acts as a amplifier.

When I look at blogs — on any topic, science, theology, parenting — that provoke rather than explore or reflect, I've noticed that they tend to have many comments. (A couple come to mind, but I find myself reluctant to name names…though it strikes me it would be an interesting experiment to stir things up and see what happens to my comment box!)

Simplifying job applications

From the perspective of all concerned [job applicants, employers, reference letter writers] the mechanics of the delivery and collation of letters of reference for job applicants can be cumbersome. This process will be made somewhat easier by a new site AcademicJobsOnline.

The only glitch I found is that when using Safari on a Mac it would not allow me to upload a letter. I tried repeatedly. I then found it worked on a Windows machine. Hopefully this was just a problem with my machine and/or it will be fixed soon.