Condensed concepts

A definitive experimental signature of the crossover from a Fermi liquid metal to a bad metal is the disappearance of a Drude peak in the optical conductivity. In single band systems this occurs in proximity to a Mott insulator and is particularly clearly seen in organic charge transfer salts and is nicely captured by Dynamical Mean-Field Theory (DMFT). An important question concerning multi-band systems with Hund's rule coupling, such as iron-based superconductors, is whether there is a similar collapse of the Drude peak. This is clearly seen in one material in a recent paper Observation of an emergent coherent state in the iron-based superconductor KFe2As2  Run Yang, Zhiping Yin, Yilin Wang, Yaomin Dai, Hu Miao, Bing Xu, Xianggang Qiu, and Christopher C. Homes Note how as the temperature increases from 15 K to 200 K that the Drude peak collapses.  The authors give a detailed analysis of the shifts in spectral weight with varying temperature by fitting the optical c

A snarky mathematician [Stanislaw Ulam] once challenged the great Paul Samuelson to name an economic proposition that is true but not obvious. Samuelson’s choice was comparative advantage , which shows, among other things, that there are mutual gains from trade even if one nation is better than another at producing everything.    Here’s a homespun illustration. Suppose a surgeon is also a whiz at house painting—better than most professional painters. Should she therefore take time off from her medical practice to paint her own house? Certainly not. For while she may have a slight edge over most painters when it comes to painting walls, she has an enormous edge when it comes to performing surgery. Surgery is her comparative advantage, so she should specialize in it and let some others, who don’t know their way around an operating room, specialize in painting—their comparative advantage. That way, the whole economy becomes more efficient.    The same principle applies to nations. E

One of most interesting new ideas about quantum matter from the last decade is that of a Hund's metal. This is a strongly correlated metal that can occurs in a multi-orbital material (model) as a result of the Hund's rule (exchange interaction) J that favours parallel spins in different orbitals. Above some relatively low temperature (i.e. compared to the bare energy scales such as non-interacting band-widths, J, and Hubbard U) the metal becomes a bad metal , associated with incoherent excitations. An important question concerns the extent to which slave mean-field theories can capture the stability of the Hund's metal, and its properties including the emergence of a bad metal above some coherence temperature, T*. In a single-band Hubbard model, the strongly correlated metallic phase that occurs in proximity to a Mott insulator is associated with a small quasi-particle weight and suppression of double occupancy, reflecting suppressed charge fluctuations. This is captur

When is a system "complex"? Even though we have intuition (e.g. complexity is associated with many interacting degrees of freedom) coming up with definitive criteria for complexity is not easy. I just finished reading, Complexity: A Very Short Introduction , by John Holland. His perspective is that a system is "complicated" if it has many interacting degrees of freedom, but is "complex" if in addition it exhibits emergent properties. The criteria for emergence is the existence of new hierarchies , containing new entities or agents (defined by the formation of  boundaries ) that are coupled by new interactions , and described by new " laws ". Holland distinguishes complex physical systems (CPS) from complex adaptive systems (CAS). The latter involve elements (agents) that can change (learn or adapt) in response to interactions with other agents. Cellular automata and pattern formation in biology are CPS, whereas genetic algorithms, econom

We all want to increase our productivity. But too often we are distracted, procrastinate, stressed, or waste time going down dead ends. I think there are two distinct kinds of productivity. The first is creative , where we can clearly conceive a project, solve a problem, or draft a useful outline. The second is the actual completion of a task , whether writing a paper or report, or making corrections, ... This is less creative and more mundane, but can consume large amounts of time, particularly if one stops and starts on the task many times. How might you increase your productivity? I think this is quite personal and maybe even somewhat random. It might be very different for different people. It can be different at different times. Factors to consider include the following. Physical space and environment.  Some people need a regular quiet work space that is free from distractions. Others will function well in a noisy cafe or an open plan office, maybe with headphones with l

As I have written many times before, water is fascinating, a rich source of diverse and unusual phenomena, and an unfortunate source of spurious research reports. Polywater is the classic example of the latter. I find the physics particularly interesting because of the interplay of hydrogen bonding and quantum nuclear effects such as zero-point motion and tunneling. There is a fascinating paper Polymorphism of Water in Two Dimensions Tanglaw Roman and Axel Groß The paper was stimulated by a Nature paper that claimed to experimentally observe square ice inside graphene nanocapillaries . Such a square structure is in contrast to the hexagonal structure found in regular three-dimensional ice. Subsequent, theoretical calculations claimed to support this observation of square ice. Here the authors use DFT-based methods to calculate the relative energies of a range of two-dimensional structures for free-standing sheets of water (both single layer and bilayers) and for sheets bounde