Condensed concepts

Previously, I considered the tricky problem of Does the doped Hubbard model superconductor? I mentioned in passing a worrying quantum Monte Carlo study published in PRB in 1999 Correlated wave functions and the absence of long-range order in numeri cal studies of the Hubbard model M. Guerrero, G. Ortiz, and J. E. Gubernatis The graph below shows the distance dependence of the pairing correlation function in the d-wave channel. If superconductivity occurs it should lend to a non-zero value equal to the square of the superconducting order parameter. It certainly looks like it tends to zero at large distances. However, careful examination shows that it seems to have a non-zero value of order 0.001. Perhaps, that is just a finite size effect. But, we should ask, " How big do we expect the long-range correlations, i.e. the magnitude of the square of the order parameter d, to be? " A cluster DMFT calculation on the doped Hubbard model (in the PRB below) gives a value

There seems to be a common view that on CVs (and grant applications) people should list the Impact Factors for each journal in which they have a paper. To me this "information" is just noise and clutter. I do not include it in my own CV or grant applications. Why? 1. IFs just encode something I know already. Nature > Science > PRL ~ JACS > Phys. Rev B ~ J. Chem. Phys. > Physica B ~ Int. J. Mod. Phys. B > Proceedings of the Royal Society of Queensland ..... 2. There is a large random element in success or failure to get an individual paper published in a high profile journal. e.g., who the referees are. 3. The average citations of a journal is not a good measure of the significance of a specific paper. There is a large variance. What really matters is how much YOUR/MY specific paper in that journal is cited in the long term. Unfortunately, in most cases it is hard to know in less than 3-5 years. 4. Crap papers can get published in Nature and Science.

Last week we struggled through chapter 4, "Renormalisation group calculations" of Hewson's book, The Kondo Problem to heavy fermions. The focus is on Kenneth Wilson's numerical treatment of the Kondo problem, mentioned in his Nobel prize citation. Much of it still remains a mystery to me... Here are a few key aspects. Please correct me where I am wrong or at least confused... First, he mapped the three-dimensional Kondo model Hamiltonian into a one dimensional tight binding chain (half-line) with single impurity spin at the boundary. This simplification makes the problem more numerically tractable. Next, he used a logarithmic discretization (in energy) of the states in the conduction band. This important step is motivated by the logarithmic divergences found by Kondo's perturbative calculation and Anderson's poor man's scaling arguments. He then numerically diagonalises the Hamiltonian with a discrete set of states for a finite chain. One then re

Weston Borden's article 40 years of fruitful chemical collaborations  has an significant observation concerning writing effective papers: focus on the physical explanation of the results rather than on the details of the methodology. He recounts how he he learnt this, while starting out as an Assistant Professor at Harvard, in a collaboration with Lionel Salem . Borden had performed some calculations using the Pariser-Parr-Pople (PPP) model for the electronic structure of conjugated organic molecules [for physicists an extended Hubbard model with long-range Coulomb interactions]. Lionel read my draft, and he promptly rewrote it. Lionel’s revised version, which was the one that we published , focused much more than my draft had on the explanation of the PPP results, rather than on the details of the calculations. This experience taught me a valuable lesson. Although describing the details of calculations and the results obtained from them is certainly important, it is even more

Many previous posts have considered how in a metallic phase close to a Mott insulator one can observe a crossover from a Fermi liquid to a bad metal with increasing temperature. One observes something quite different in FeSi (iron silicide) which has been a subject of debate for several decades. Different paper titles include the following words: Kondo insulator, ferromagnetic semiconductor, unconventional charge gap, strong electron-phonon coupling, Anderson-Mott localization, singlet semiconductor, covalent insulator, correlated band insulator, ferromagnetic metal, .... At low temperatures FeSi is a semiconductor with a gap of about 50 meV (500 K). Both the spin susceptibility and the resistivity are gapped. However,  around 200 K there is a crossover to a bad metal. The spin susceptibility has a maximum versus temperature around 400 K and above that can be fitted to a Curie-Weiss form, suggesting the presence of local moments. The thermopower has a maximum around 50 K with a c

There is a very nice article in the Journal of Organic Chemistry With a Little Help from My Friends: Forty Years of Fruitful Chemical Collaborations by Weston Thatcher Borden Borden's career is unusual in that he has done both organic synthesis [i.e., actually making molecules] and computational quantum chemistry. The article is worth reading for several reasons. It describes some -interesting organic chemistry and shows how quantum chemistry has illuminated it -characteristics of fruitful collaborations, both between theorists and between theorists and experimentalists -interesting history and personal vignettes and perspectives On the latter I found the following throwaway line rather disturbing and disappointing: When I was an Assistant Professor at Harvard, unlike most of my colleagues in the Chemistry Department, Bill Doering   seemed genuinely interested in talking about chemistry with me. Unfortunately, this happens too often. I would be curious to know why

Topological insulators (TIs) are certainly a hot topic. However, there are two things that might make one nervous about all the excitement. 1. All the materials being studied as TIs [e.g. Bi2Se3] actually aren't TIs. What!? A TI is by definition a bulk insulator  with surface metallic states that are topologically protected. However, the actual materials turn out not to be bulk insulators. On a practical level this makes separating out bulk and surface contributions, particularly in transport measurements, tricky. But, also presents an ideological problem: one is not actually studying the phase of matter one wishes one was studying. 2. One could argue that TIs are "just a band structure effect", i.e., they do not involve any quantum many-body physics. However, these objections are put to rest by a preprint Discovery of the First True Three-Dimensional Topological Insulator: Samarium Hexaboride Steven Wolgast, Cagliyan Kurdak, Kai Sun, J. W. Allen, Dae-Jeong Kim,

There is a paper in Science this week  Flows of Research Manuscripts Among Scientific Journals Reveal Hidden Submission Patterns The authors claim,  Resubmissions were significantly more cited than first-intents published the same year in the same journal....  ... these results should help authors endure the frustration associated with long resubmission processes and encourage them to take the challenge  Then I looked at the data below to see how strong the claimed effect was. I think the horizontal lines mark the mean and the box shows the variance. Hence, it looks to me like citations may increase by less than 10% with resubmission. This hardly seems on any significance to me. But, am I missing something? Maybe this is another issue of comparisons are in the eye of the beholder  or the silly claims that journals make about their impact factors or some faculty make about their student evaluations.

Chapter 3 of Hewson's The Kondo Problem to Heavy fermions reviews Anderson's poor man's scaling treatment of the Kondo model. Starting with the anisotropic Kondo Hamiltonian one rescales the electronic bandwidth D and see how the interactions J_z and J_ and J+ rescale. To lowest order in perturbation theory this leads to the renormalisation group equations Solving these gives the flow diagram below A few important consequences 1. Antiferromagnetic (AFM) interactions flow to strong coupling. 2. The Kondo energy/temperature is invariant to the flow. 3. This is an example of asymptotic freedom  [interactions can weaker at higher energies]. It is impressive that Anderson did this before Wilson and Fisher used renormalisation group ideas to describe critical phenomena in classical phase transitions. It is fascinating that the same flow equations and flows describe the Kosterlitz-Thouless phase transition  associated with topological order [vortex p

I can fully imagine a grant reviewer, tenure or hiring committee saying that when reviewing the "impact" of a particular publication of an individual. Furthermore, one can also say "the paper was in PRL but it was a full 12 months between submission and publication. Clearly, he was lucky to get in PRL at all..." But, there is a problem with all this. These observations apply to Duncan Haldane's 1988 paper  Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane's paper has been receiving about 100 citations per year for the past few years. It now has a total of 530 citations in Physical Review journals. However, from 1988 to 1999 it received only 17 citations. Hardly impressive.

Last week we read "Beyond perturbation theory", chapter 3 of Hewson's The Kondo Problem to Heavy Fermions. First he gives, without derivation, perturbation expressions for the impurity spin susceptibility and specific heat. The results exhibit logarithmic divergences at temperatures of the order of the Kondo temperature. Hewson discusses some of the herculean efforts in the 1960s of people such as Abrikosov, Suhl, and Hamann, to come up with new diagrammatic techniques and summations to get rid of, or at least reduce, the divergences. The results still have logarithmic temperature dependences. None give the Fermi liquid like dependences at low temperatures that experiments hinted at. The Kondo effect is non-perturbative . n.b. the Kondo temperature has a non-analytic dependence on J. What does one do? An important insight was variational wave function proposed by Yosida in 1966. One finds that the ground state is a spin singlet between the impurity spin and a

Seth Olsen  and I are about to advertise for a postdoc to work with us at UQ. The flavour of our interests and approach can be seen in posts on this blog under labels such as  organic photonics ,  quantum chemistry , conical intersections, and Born-Oppenheimer approximation. A draft of the official position description is here . We anticipate an official advertisement will appear shortly. Please contact us if you are interested.

Some of my colleagues, may say "Yes!". However, this post is mostly concerned with moving from academia to industry and is mostly directed at graduate students and postdocs. However, some of the issues are also relevant to faculty considering a change of institution. The issues are based on my limited experience and observations over almost three decades. I stress that I am not saying that all the realities below are right or just, only that they are realities that may need to be faced. Its personal. Different people have different values. How much do you value (or don't value) independence, freedom, money, family time, flexible work hours, job "security", affirmation, geographic location, ....? The relative value you place on such things will significantly affect what job may be suitable for you and whether and when you decide to make a change? A job that is great for your friend may be horrible for you and visa versa. There is no simple right answer.

This post follows up on earlier posts including Connecting the pseudogap to superconductivity in the organics There is a nice paper Pseudogap and Fermi arc in κ-type organic superconductors by Jing Kang, Shun-Li Yu, Tao Xiang, and Jian-Xin Li They use Cluster Perturbation Theory to study the Hubbard model on the anisotropic triangular lattice at half filling. They calculate the one-electron spectral function using clusters as large as 12 sites [embedded self-consistently in an infinite lattice]. The authors find three distinct phases: Mott insulator, Fermi liquid, and a pseudogap state with Fermi arcs. The latter occurs in between the two other phases. The Figure below shows an intensity map of the spectral function at the Fermi energy for U=4t and t'=0.7t. This clearly shows a complete Fermi surface (with hot spots). As U increases towards the Mott phase, U=5t one sees parts of the Fermi surface gap out leaving Fermi arcs. Note the cold spots [red region=low scatteri

Chapter 2 of Alex Hewson's The Kondo problem to heavy fermions reviews what Kondo actually did to get his name on the problem. Here is a brief summary of the highlights from last weeks reading group. He considered the experimental data on the temperature dependence of the resistivity of metals containing magnetic impurity atoms. It was particularly puzzling that there was a minimum. Generally, one expects scattering (and thus resistivity) to increase with increasing temperature. First, Kondo recognised that the experimental data suggested that it was a single impurity problem , i.e, one could neglect interactions between the impurities. Second, the effect seemed to scale with magnitude of the local magnetic moments. This led him to consider the simplest possible model Hamiltonian  the s-d model proposed by Zener in 1951, but now known as the Kondo model. According to Boltzmann/Drude/Kubo at low temperatures the resistivity of a metal is proportional to the rate at which el

It is a natural human tendency to compare oneself to ones peers. I suggest that this can be quite unhelpful for your mental health and for harmonious relationships. A natural consequence of such comparisons may be discouragement or hubris depending on your personality. Grad students and postdocs may compare hours worked, numbers of papers, number of interviews, numbers of invited conference talks, attention from their advisor.... Faculty may compare total funding, size of their latest grant, numbers of students, size of office, speed of promotion, h-index, lab space, ... This can lead to bitterness and friction. When I was younger I struggled due to making such comparisons. Mostly they led to unnecessary anxiety and discouragement. Furthermore, with hindsight my "metrics" turned out to be pretty irrelevant indicators of future success [i.e. survival] in science. I never considered luck , perseverance, flexibility, passion, communication and personal skills... Now

There is a nice paper Pseudogap temperature as a Widom line in doped Mott insulators by Giovanni Sordi, Patrick Sémon, Kristjan Haule, and Andre-Marie Tremblay The abstract ends with the important and articulate claim: Broken symmetry states appear in the pseudogap and not the other way around. The figure below shows the phase diagram that the authors calculated for the doped Hubbard model with cluster DMFT. The key point is that at low temperatures there is a first-order phase transition from the pseudogap to a correlated Fermi liquid. Furthermore, there is no symmetry breaking associated with this transition. In this respect the phase diagram is analogous to a liquid-vapour transition in a simple fluid and so the authors identify the metal-pseudogap crossover line with the Widom line for the former class of transitions. This is an elegant new idea. In the actual materials this first-order transition is masked by the presence of superconductivity. Surely, th

When I was a grad student at Princeton, Phil Anderson had a number of students (Zhou Zou, Ted Hsu, Joe Wheatley, ...) who worked on RVB theory. They all eventually left physics for Wall Street. Phil used to joke that they were all making more money than him! I just learned that Ted Hsu is now a member of parliament in Canada! I saw this in an article in Physics Today that raises concerns about changes in funding direction for physics in Canada. There is also an interview with him on the Physics Today site.

Jure Kokalj and I just finished a paper Thermodynamics of a bad metal-Mott insulator transition in the presence of frustration We study the temperature dependence of a range of thermodynamic properties (charge susceptibility, specific heat, entropy and spin susceptibility) of the Hubbard model on the anisotropic triangular lattice at half filling by means of the numerical finite-temperature Lanczos method. This Hubbard model describes several important families of superconducting organic charge transfer salts. The results include Clear signatures of a metal-Mott insulator transition in the charge susceptibility. The metal-insulator transition can be driven either by increasing interactions or by reducing frustration. The metallic phase is characterized by a small charge susceptibility, large entropy, low coherence temperature, large renormalized quasiparticle mass, and large spin susceptibility. The coherence temperature corresponds to destruction of quasi-particles and cross

Yes. According to a nice review by Yu, Si, Goswami, and Abrahams. A key piece of the evidence for strong correlations is recent inelastic neutron scattering experiments reported in this Nature Physics paper . They show that even in the superconducting materials [which are doped from parent Antiferromagnetic compounds] there are sizeable fluctuating magnetic moments. The figure below shows the dynamical spin susceptibility versus energy. For both superconducting and antiferromagnetic materials the susceptibility is essentially the same for energies above 100 meV. The area under the curve is equal to the square of the fluctuating local moment. The magnitude is a few Bohr magnetons, as one would expect in a doped Mott insulator. Furthermore, a weak coupling RPA treatment [which is invoked to explain the superconductivity] cannot capture the magnitude of these spin fluctuations. In contrast, a DMFT treatment from Park, Haule, and Kotliar  is consistent with the experimental data,

The thermoelectric power of a metal is rather complex. Even Ashcroft and Mermin suggested that it was difficult to interpret and relate to the theoretical calculations. Earlier posts have considered some of the subtleties, particularly in strongly correlated electron systems. To me a couple of recent experimental papers present beautiful data but are not cautious enough in their interpretation. They need to rule out alternative explanations [see below] before I will be convinced of the explanations that they propose. Fermi-surface reconstruction by stripe order in cuprate superconductors F. Laliberté, J. Chang, N. Doiron-Leyraud, E. Hassinger, R. Daou, M. Rondeau, B.J. Ramshaw, R. Liang,  D.A. Bonn, W.N. Hardy, S. Pyon, T. Takayama, H. Takagi, I. Sheikin, L. Malone, C. Proust, K. Behnia, and Louis Taillefer They observe a sign change in the thermopower and associate this with a Fermi surface reconstruction, stripe formation, and a quantum phase transition. Spin fluctuati

Yesterday the Australian Research Council announced which grant applications were successful for funding for next year. So roughly 20 per cent of people were happy and 80 per cent were sad. After the exhilaration or devastation inevitably come the post-mortems, particularly from those who are unsuccessful. We offer each other a multitude of possible reasons for failure or for success.... Professor Z was on the committee and he doesn't like my field.... All they care about is number of publications.... I need to increase my h-index...  They must have liked the bit I wrote about... Clearly they don't like people who work at the interface of chemistry and physics... I need more Nature papers.... I should have promised less... It is because I did not have a big name person on the grant... it is because I am working on such a hot topic.... Obviously they aren't going to fund 2 groups working in my area.... I think Dr. X must have been that negative referee...People think my grou

In the reading group this past week we finished the first chapter of Hewson's The Kondo problem to heavy fermions . There is a bit of a narrative which I will try to highlight. A key aspect is getting to the Kondo Hamiltonian which describes a single magnetic impurity spin interacting with a band of conduction electrons. Where does this come from? What is the physical origin of the local magnetic moment? To understand this one needs to look at the Anderson model Hamiltonian. Key physics is associated with the Coulomb repulsion U [aka Hubbard] associated with two electrons on the localised orbital associated with the impurity. First, if one solves the model in the mean-field [Hartree-Fock] approximation one finds that a net magnetic moment can occur, i.e. spin rotational symmetry is broken, for certain parameter regimes. This result was half of Anderson's 1978 Nobel Prize. Second, one can derive the Kondo Hamiltonian as an effective Hamiltonian for the Anderson mod

Sometimes postdocs are given the opportunity to teach part [or all] of an undergraduate or graduate course, even though this is not part of their job description. At UQ there is a formal university wide program ResTeach which aims to get research staff [including senior faculty such as myself] involved in teaching. If you are a postdoc, should you do it? Should faculty who pay the salaries of postdocs from their grants encourage or discourage this? Here are some of the significant advantages to a postdoc of doing some teaching: Having the experience listed on your CV may help you get a faculty position at some institutions. For example, in Australia this seems to be almost a pre-requisite these days. Furthermore, if you can be innovative, get high student evaluations, and/or boost enrolments that may be viewed very favourably. You usually learn a lot of science from teaching, even lower level courses. It can be enjoyable and satisfying. If you are fortunate enough to even

Answer this question is difficult and controversial. There is a nice review Numerical studies of the 2D Hubbard model by Doug Scalapino which considers the question. He claims that in the end the answer is yes. However, there are several subtleties along the way. I just mention two that I learnt. To attempt to answer the question one calculates the d-wave pairing susceptibility on a finite lattice. In determinantal Monte Carlo [which acts in imaginary time and does have an increasing sign problem with decreasing temperature] one observes that as the temperature (=1/beta) decreases the pairing susceptibility increases. This is encouraging. Except, ... Puzzle/caution/subtlety  I the pairing susceptibility is less than for U=0!  Clearly there is no superconductivity for U=0 and a key claim of the Anderson paradigm is that large U and correlations are the key for high-Tc. So what is going on? Scalapino and his collaborators argue that this decrease with increasing U is becaus

The trivial problem is that I find reading the papers of Nozieres difficult and exhausting. They are big on hand waving and physical insight. An earlier post considered his classic paper on a Fermi liquid treatment of the Kondo problem. Now the real problem. Today I giving a cake meeting talk about a short 2005 paper Kondo lattices and the Mott Metal-Insulator which Nozieres published in a JPSJ volume "Kondo effect- 40 years after the discovery". It also has several other nice (short) review articles. This paper reviews the resolution of the " exhaustion problem " for Kondo lattices, first raised by Nozieres in a 1998 paper. In the Kondo effect a single magnetic impurity forms a spin singlet with a collection of metallic electrons within an energy range T_K (the Kondo temperature) of the Fermi energy, E_F. Typically, T_K is much smaller than E_F. Now consider the Kondo lattice where there are magnetic "impurities" (i.e. localised spins) placed on a