Condensed concepts

According to blogspot here are the six most popular posts from this blog over the past year Effective "Hamiltonians" for the stock market Thirty years ago in Princeton Relating non-Fermi liquid transport properties to thermodynamics  Mental health talk in Canberra What simple plotting software would you recommend? A political metaphor for the correlated electron community Thanks to my readers, particularly to those who write comments. Best wishes for the New Year!

Previously I posted about a laundry detergent that had "Vibrating molecules" [TradeMark]. Here is a product my son recently bought that benefits from "Invisible science" [TradeMark]. I welcome guesses as to what the product.

The American Physical Society has prepared a draft statement calling on all universities "to provide all physics and astronomy majors with significant research experiences". The statement is worth reading because of the claims and documentations about some of the benefits of such experiences. In particularly, such experiences can better prepare students for a broad range of career options. I agree. However, I add some caveats. I think there are two dangers that one should not ignore. First, departments need to be diligent that students are not just used as "cheap labour" for some faculty research. Earlier I posted about What makes a good undergraduate research project? , which attracted several particularly insightful comments. Second, such undergraduate research experiences are not a substitute for an advanced undergraduate laboratory.  APS News recently ran a passionate article, Is there a future for the Advanced Lab?  by Jonathan Reichert. It is very tempt

Just because you read something in a chemistry textbook does not mean you should believe it. Basic [pun!] questions about what happens to H+ ions in acids remain outstanding. Is the relevant unit H3O+, H5O2+ [Zundel cation], H9O4+ [Eigen cation], or something else? There is a fascinating Accounts of Chemical Research Myths about the Proton. The Nature of H+ in Condensed Media Christopher A. Reed Here are a few highlights. H+ must be solvated and is nearly always di-ordinate, i.e. "bonded" to two units. H3O+ is a rarely seen. "In contrast to the typical asymmetric H-bond found in proteins (N–H···O) or ice (O–H···O), the short, strong, low-barrier (SSLB) H-bonds found in proton disolvates, such as H(OEt2)2+ and H5O2+, deserve much wider recognition.'' This is particularly interesting because quantum nuclear effects are important in these SSLBs. A poorly understood feature of the IR spectra of proton disolvates in condensed phases is that IR bands assoc

A good principle in science is "extra-ordinary claims require extra-ordinary evidence", i.e. the more exotic and unexpected the claimed new phenomena the greater the evidence needs to be before it should be taken seriously. A classic case is the recent CERN experiment claiming to show that neutrinos could travel faster than the speed of light. Surely it wasn't too surprising when it was found that the problem was one of detector calibration. Nevertheless, that did not stop many theorists from writing papers on the subject. Another case, are claims of "quantum biology". About a decade ago some people tried to get me interested in some anomalous experimental results concerning elastic scattering of neutrons off condensed phases of matter. They claimed to have evidence for quantum entanglement between protons on different molecules for very short time scales and [in later papers] to detect the effects of decoherence on this entanglement. An example is this PRL  w

No. Someone can write a brilliant paper and yet poorly reference previous work. On the other hand, one can write a mediocre or wrong paper and reference previous work in a meticulous manner. But, I have to confess I find I sometimes do judge a paper by the quality of the referencing. I find there is often a correlation between the quality of the referencing and the quality of the science. Perhaps this correlation should not be surprising since both reflect on how meticulous is the scholarship of the authors. If I am sent a paper to referee I often find the following happens. I desperately search the abstract and the figures to find something new and interesting. If I don't I find that sub-consciously I start to scan the references. This sometimes tells me a lot. Here are some of the warning signs I have noticed over the years. Lack of chronological diversity. Most fields have progressed over many decades. Yet some papers will only reference papers from the last few year

A size-able amount of time and energy has been spent by the "hard condensed matter" community over the past quarter century studying unconventional superconductors. A nice and recent review is by Mike Norman.  In the absence of spin-orbit coupling spin is a good quantum number and the Cooper pairs must either be in a spin singlet or a spin triplet state. Furthermore, in a crystal with inversion symmetry spin singlets (triplets) are associated with even (odd) parity. Actually, pinning down the symmetry of the Cooper pairs from experiment turns out to be extremely tricky. In the cuprates the "smoking gun" experiments that showed they were really d-wave used cleverly constructed Josephson junctions, that allowed one to detect the phase of the order parameter and show that it changed sign as one moved around the Fermi surface. How can one show that the pairing is spin triplet? Perhaps the simplest way is to show that they have an upper critical magnetic field that

Roald Hoffmann and Sason Shaik are two of my favourite theoretical chemists. They have featured in a number of my blog posts. I particularly appreciate their concern with using computations to elucidate chemical concepts. In Angewandte Chemie there is a fascinating article, One Molecule, Two Atoms, Three Views, Four Bonds that is written as a three-way dialogue including Henry Rzepa. The simple (but profound) scientific question they address concerns how to describe the chemical bonding in the molecule C2 [i.e. a diatomic molecule of carbon]. In particular, does it involve a quadruple bond? The answer seems to be yes, based on a full CI [configuration interaction] calculation that is then projected down to a Valence Bond wave function. The dialogue is very engaging and the banter back and forth includes interesting digressions such the role of Rzepa's chemistry blog , learning from undergraduates, the relative merits of molecular orbital theory and valence bond theory, the

This week three excellent articles have been brought my attention that highlight current problems with science and academia. The first two are in the Guardian newspaper. How journals like Nature, Cell and Science are damaging science The incentives offered by top journals distort science, just as big bonuses distort banking Randy Schekman, a winner of the 2013 Nobel prize for medicine. Peter Higgs: I wouldn't be productive enough for today's academic system Physicist doubts work like Higgs boson identification achievable now as academics are expected to 'keep churning out papers' How academia resembles a drug gang  is a blog post by Alexandre Afonso , a lecturer in Political Economy at Kings College London. He takes off from the fascinating chapter in Freakanomics, "Why drug dealers still live with their moms." It is because they all hope they are going to make the big time and eventually become head of the drug gang. Academia has a similar hierarchic

When I recently gave a talk on bad metals in Sydney at the Gordon Godfrey Conference, Andrey Chubukov and Janez Bonca asked some nice questions that stimulated this post. The main question that the talk is trying to address is: what is the origin of the low temperature coherence scale T_coh associated with the crossover from a bad metal to a Fermi liquid? In particular,  T_coh is much less than the Fermi temperature of for non-interacting band structure of the relevant Hubbard model [on an anisotropic triangular lattice at half filling]. Here is the key figure from the talk [and the PRL written with Jure Kokalj]. It shows the temperature dependence of the specific heat for different values of U/t for a triangular lattice t'=t. Below T_coh, the specific heat becomes approximately linear in temperature. For U=6t, which is near the Mott insulator transition, T_coh ~t/20. Thus, we see the emergence of the low energy scale. Note that well into the Mott phase [U=12t] there i

This past year I have been surprised and encouraged that this blog has a wide readership. However, I have also learnt that I don't want it to become too popular. A few months ago, when I was visiting Columbia University I met with Peter Woit. He writes a very popular blog, Not Even Wrong , that has become well known, partly because of his strong criticism of string theory. It is a really nice scientific blog, mostly focusing on elementary particle physics and mathematics. The comments generate some substantial scientific discussion. However, it turns out that the popularity is a real curse.   A crowd will attract a bigger crowd. The comments sections attracts two undesirable audiences. The first are non-scientists who have their own "theory of everything" that they wish to promote. The second "audience" are robots that leave "comments" containing links to dubious commercial websites. Peter has to spend a substantial amount of time each day monitorin

Understanding the unique properties of water remains one of the outstanding challenges in science today. Most discussions and computer simulations of pure water [and its interactions with biomolecules] treat the nuclei as classical. Furthermore, the hydrogen bonds are classified as weak. Increasingly, these simple pictures are being questioned. Water is quantum! There is a nice PNAS paper  Nuclear quantum effects and hydrogen bond fluctuations in water Michele Ceriotti, Jerome Cuny, Michele Parrinello, and David Manolopoulos The authors perform path integral molecular dynamics simulations where the nuclei are treated quantum mechanically, moving on potential energy surfaces that are calculated "on the fly" from density functional theory based methods using the Generalised Gradient Approximation. A key technical advance is using an approximation for the path integrals (PI) based on a mapping to a Generalised Langevin Equation [GLE] [PI+GLE=PIGLET!]. In the figure below

On the arXiv, Andre-Marie Tremblay has posted a nice tutorial review  Strongly correlated superconductivity . It is based on some summer school lectures and will be particularly valueable to students. I think it is particularly clearly and nicely highlights some key concepts.  For example, the figure below highlights a fundamental difference between a Mott-Hubbard insulator and a band insulator [or semiconductor]. There is also two clear messages that should not be missed. A minority of people might disagree. 1. For both the cuprates and large classes of organic charge transfer salts the relevant effective Hamiltonians are "simple" one-band Hubbard models. They can capture the essential details of the phase diagrams, particularly the competition between superconductivity, Mott insulator, and antiferromagnetisim. 2. Cluster Dynamical Mean-Field Theory (CDMFT) captures the essential physics of these Hubbard models. I agree completely. Tremblay does mention some

Sometimes when I am at a conference or in a seminar I find that I have absolutely no idea what the speaker is talking about. It is not just that I don't understand the finer technical details. I struggle to see the context, motivation, and background. The words are just jargon and the pictures are just wiggles and the equations random symbols. What is being measured or what is being calculated? Why? Is there a simple physical picture here? How is this related to other work? A senior experimental colleague I spoke to encouraged me to post this. He thought that his similar befuddlement was because he wasn't a theorist. There are three audiences for this message. 1. Me. I need to work harder at making my talks accessible and clear. 2. Other speakers. You need to work harder at making your talks accessible and clear. 3. Students. If you are also struggling don't assume that you are stupid and don't belong in science. It is probably because the speaker is doing a po

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.

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.

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 conti

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

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.

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 fr

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

Recently, I posted about a laundry detergent I bought in India that features "Vibrating molecules" (TM) and wryly commented that the marketing of some universities is not much better. I saw that this week, again in India. I read that  a former Australian cricket captain,  Adam Gilchrist , [an even bigger celebrity in India than in Australia], was in Bangalore as a "Brand name Ambassador" for a particular Australian university. The university annually offers one   Bradman scholarship to an Indian student for which it pays 50 per cent of the tuition for an undergraduate degree. [Unfortunately, the amount of money spent on the business class airfares associated with the launch of this scholarship probably exceeded the annual value of the scholarship]. Some measure of Gilchrist's integrity is that at the same event sponsored by the university he said he supported the introduction of legalised betting on sports in India . Many in Australia think such betting has

There is a nice review article Low-barrier hydrogen bonds in proteins by M.V. Hosur, R. Chitra, Samarth Hegde, R.R. Choudhury, Amit Das, and R.V. Hosur Most hydrogen bonds in proteins are weak, as characterised by a donor-acceptor distance larger than 2.8 Angstroms, and interaction energies of a few kcal/mol (~0.1 eV~3 k_B T). However, there are some bonds that are much shorter. In particular, Cleland proposed in 1993 that for some enzymes that there are H-bonds that are sufficiently short (R ~ 2.4-2.5 A) that the energy barrier for proton transfer from the donor to acceptor is sufficiently small that it is comparable to the zero-point energy for the donor-H stretch vibration. These are called low-barrier hydrogen bonds. This proposal remains controversial. For example, Ariel Warshel says they have no functional role. The authors perform extensive analysis of crystal structure databases, for both proteins and small molecules, in order to identify the relative abundance of short b

Tomorrow I am giving the  theory colloquium at the Tata Institute for Fundamental Research in Mumbai . My host is Kedar Damle . Here are the slides for " Frustrated Mott insulators: from quantum spin liquids to superconductors ". A related review article was co-authored with Ben Powell.

Previously I have argued that Science is broken and raised the question,  Have journals become redundant and counterproductive? . Reading these earlier posts is recommended to better understand this post. Some of the problems that need to be addressed are: journals are wasting a lot of time and money rubbish and mediocrity is getting published, sometimes in "high impact" journals honorary authorship leads to long author lists and misplaced credit increasing emphasis on "sexy" speculative results metrics are taking priority over rigorous evaluation negative results or confirmatory studies don't get published lack of transparency of the refereeing and editorial process ..... These problems are serious and need to be addressed by the scientific community. It is better we address them before "solutions" be imposed on us by politicians and administrators. It is always much easier to identify problems than to provide constructive and realisti

This follows an earlier post Emergence of dynamical particle-hole asymmetry  concerning the new approach of Sriram Shastry to doped Mott insulators, describing them as an extremely correlated Fermi liquid, and characterised by two self energies. There is a nice preprint Extremely correlated Fermi liquid theory meets Dynamical mean-field theory: Analytical insights into the doping-driven Mott transition Rok Zitko, D. Hansen, Edward Perepelitsky, Jerne Mravlje, Antoine Georges, Sriram Shastry The part ice-hole asymmetry means that electron-like quasi-particles have much longer lifetimes than hole-like quasi-particles. This means that the imaginary part of the (single-particle Dyson) self energy Sigma(omega) is asymmetric about omega=0, the chemical potential. Here are two particularly note-worthy figures from the paper. The first shows how the asymmetry at omega=0 is associated with the quasi-particle band (QPB) at the top of the lower Hubbard band (LHB). This band emerges as th

This week I bought this laundry detergent in India Note how at the bottom it features the TradeMark, " Vibrating molecules ", giving it Power! It is interesting/amusing to read the Wikipedia page for Surf Excel . It is full of similar marketing nonsense. Scientists might mock this, but some university marketing campaigns are comparable.

There is a very thoughtful article in Angewandte Chemie The Seven Sins in Academic Behavior in the Natural Sciences by Wilfred F. van Gunsteren It is worth reading slowly and in full. He highlights the negative influence of "high impact" journals and discusses many of the same issues as the recent cover story in the Economist. He has some nice examples of each of seven sins. But, there was one paragraph that really stood out. Administrative officials at universities and other academic institutions should refrain from issuing detailed regulations that may stifle the creativity and adventurism on which research depends. They should rather foster discussion about basic principles and appropriate behavior, and judge their staff and applicants for jobs based on their curiosity-driven urge to do research, understand, and share their knowledge rather than on superficial aspects of academic research such as counting papers or citations or considering a person’s grant income

Here are a couple of things I find surprising about the electronic transport properties of materials. 1. One cannot simply have materials, particularly metals, that have any value imaginable for a transport coefficient. For example, one cannot make the conductance or the thermopower as large as one wishes by designing some fantastic material. 2. Quantum mechanics determines what these fundamental limits are. Furthermore, the limiting values of transport coefficients are often set in terms of fundamental constants [Planck's constant, Boltzmann's constant, charge on an electron]. The fact that this is profound is indicated by the fact that this was not appreciated until about 25 years ago. A nice clean example is the case of a  quantum point contact with N channels. The conductance must be N times the quantum of conductance, 2e^2/h. This result was proposed by Rolf Landauer  in 1957 but many people did not believe it until the first experimental confirmation in 1988. Th

When I was in Slovenia a few weeks ago I spent a nice afternoon at the National Institute of Chemistry discussing hydrogen bond dynamics and spectroscopy with Jernez Stare and Joze Grdadolnik. Janez Mavri was busy fielding phone calls from the press about his collaborator Ariel Warshel who had been awarded the Nobel Prize in Chemistry the previous day. I also met Dusan Hadzi, who was a real pioneer in hydrogen bond studies. He is now 92 years old but still comes into the lab each day, and is working on a several papers with younger collaborators! Of particular interest are the Car-Parrinello simulations of sodium hydrogen bissulfate performed by Gordana Pirc, Stare, and Mavri. This crystal has an O...O distance of R=2.432 Angstroms with slightly asymmetric O-H distances of r=1.156 and 1.276 A. The Car-Parrinello runs show R fluctuating between 2.24 and 2.69 A! Snapshots of the associated one-dimensional potentials for the OH stretch are shown below. For each potential they

Enrico Fermi told Freeman Dyson  " with four parameters I can fit an elephant, and with five I can make him wiggle his trunk". Phil Nelson  kindly brought to my attention a nice paper Drawing an elephant with four complex parameters by Jürgen Mayer, Khaled Khairy, and Jonathon Howard There is also an interactive Mathematica Demonstration that allows you to see how the quality of the fit increases with the number of parameters [but does not have a wiggling trunk!].

Is there any difference in the nature of emergence in quantum and classical systems? What is the difference between strong and weak emergence? An emergent property of a system is one that is: a. not present in the individual components of the system b. difficult to predict a priori  from a knowledge of the components and their interactions c. independent of the finer details of the components Equivalently emergent properties are a. qualitatively different b. usually discovered empirically and sometimes are given a reductionist explanation a posteriori c. universal and stable to perturbations This can be illustrated with the rigidity of a solid a. the individual atoms that make up a solid are not rigid. b. elasticity theory preceded crystallography c. all solids are rigid, regardless of their chemical composition. Emergence occurs in both quantum and classical systems.  The properties that emerge can be distinctly different.  Superconductivity  and superfluidity are in

Science is all about creating reliable and reproducible knowledge. The Economist has a cover story How science goes wrong. It is worth reading, pondering, and discussing. I agree with the general observations of the article. Unfortunately, some of my worst fears are confirmed. Some of the problematic issues that are highlighted have been discussed on this blog before. Problems discussed include: the career pressure to publish leading to a lot of low quality work the pre-occupation with "sexy"new results that can be published in high profile journals poor quality of refereeing, meaning many erroneous papers get published there are few papers about negative results because they are hard to get published there are few papers testing/confirming the results in other papers because they attract little attention I like the article because it is constructive in proposing reform, particularly from within science, and does discuss various initiatives, including some funded

There is a nice preprint  Universal thermopower of bad metals Veljko Zlatic, G.R. Boyd, Jim Freericks It contains calculations of the temperature and doping dependence of the thermoelectric power for the Falicov-Kimball model within the approximation of Dynamical-Mean Theory [DMFT]. This spinless fermion model is even "simpler" than the Hubbard model. Yet it captures some of the same physics, particularly the Mott metal-insulator transition. It also has the advantage that DMFT has an exact analytical solution. One does not need an "impurity solver", such as for the Hubbard model. There is an extensive Rev. Mod. Phys. on this, by Freericks and Zlatic. Below I discuss one significant disadvantage of the model. The figure below shows the calculated temperature dependence of the thermopower for several different dopings. The solid lines are the result from the Kubo formula [essentially exact] and the dashed line is the approximate Kelvin formula [the derivati

If there is any one individual who has influenced both the scientific content and philosophy of this blog it is Phil Anderson. There are 45 posts with "P.W. Anderson" as a label, more than any other individual. However, his influence goes far beyond that. In December Princeton will host a 90th birthday celebration conference  in his honour.