A critical review of holographic claims about condensed matter

There is a very helpful review article
Demystifying the Holographic Mystique by Dmitri Khveshchenko

In order to motivate a proper full reading I just give a few choice quotes.

Thus far, however, a flurry of the traditionally detailed (hence, rarely concise) publications on the topic have generated not only a good deal of enthusiasm but some reservations as well. Indeed, the proposed ’ad hoc’ generalizations of the original string-theoretical construction involve some of its most radical alterations, whereby most of its stringent constraints would have been aban- doned in the hope of still capturing some key aspects of the underlying correspondence. This is because the target (condensed matter) systems generically tend to be neither conformally, nor Lorentz (or even translationally and/or rotationally) invariant and lack any supersymmetric (or even an ordinary) gauge symmetry with some (let alone, large) rank-N non-abelian group. 

Moreover, while sporting a truly impressive level of technical profess, the exploratory ’bottom-up’ holographic studies have not yet helped to resolve such crucially important issues as: 

• Are the conditions of a large N, (super)gauge sym- metry, Lorentz/translational/rotational invariance of the boundary (quantum) theory indeed necessary for establishing a holographic correspondence with some weakly coupled (classical) gravity in the bulk? 

• Are all the strongly correlated systems (or only a precious few) supposed to have gravity duals? 

• What are the gravity duals of the already documented NFLs? 

• Given all the differences between the typical condensed matter and string theory problems, what (other than the lack of a better alternative) justifies the adaptation ’ad verbatim’ of the original (string-theoretical) holographic ’dictionary’? 

and, most importantly: 

• If the broadly defined holographic conjecture is indeed valid, then why is it so? 

Considering that by now the field of CMT holography has grown almost a decade old, it would seem that answering such outstanding questions should have been considered more important than continuing to apply the formal holographic recipes to an ever increasing number of model geometries and then seeking some resemblance to the real world systems without a good understanding as to why it would have to be there in the first place. In contrast, the overly pragmatic ’shut up and calculate’ approach prioritizes computational tractability over phys- ical relevance, thus making it more about the method (which readily provides a plethora of answers but may struggle to specify the pertinent questions) itself, rather than the underlying physics.

Why are quantum gases called degenerate?

In my recent tutorial on bad metals at IISER Pune a student asked me a basic question that I could not answer:
"Why is the degenerate Fermi gas called "degenerate"?
Is it anything to do with degenerate energy levels?"

So, I went in search for answers.

The Wikipedia entry on Degenerate matter is a bit rambling and I found it unhelpful.

I then went to the library and looked at a few textbooks and found a range of answers. Some books use the term "degenerate" without any elaboration.

In the discussion below it seems looking at the Oxford dictionary is helpful:

Having lost the physical, mental, or moral qualities considered normal and desirable; showing evidence of decline. 

technical: Lacking some usual or expected property or quality, in particular.

Here are a few entries

degenerate. (This use of the word is completely unrelated to its other use to describe a set of quantum states that have the same energy).

Daniel V. Schroeder, An Introduction to Thermal Physics, page 272.
[my favourite undergraduate text on statistical mechanics]

... a bit of terminology. At low temperature, quantum ideal gases behave very differently from the way a classical ideal gas behaves. ..... The quantum gases are said to be degenerate at low temperatures. This is not a moral judgement. Rather, the word "degenerate" is used in the sense of departing markedly from the properties of an "ordinary" classical gas.

Ralph Baierlein, Thermal Physics, page 192.

Gas degeneration proper. The quantitative study of the deviations from the classical gas laws when xi is not very small ...

Erwin Schrodinger, Statistical Thermodynamics (1936)

Here xi is the product of the particle density and the thermal deBroglie wave length cubed.

The definition of a quantum gas is one where xi becomes larger than one. (This occurs for "high" densities and "low" temperatures).

But then there is an interpretation in terms of degeneracy of energy levels because one can consider the case where each energy level has degeneracy g and condition for a non-degenerate gas (i.e. Maxwell-Boltzmann statistics to apply) is
g >> n_i ~ exp ((mu-Ei)/kB T) = number of particles in level i

I welcome comments.

Deconstructing noise in organic charge transfer salts

There are several things that I used to find very puzzling about electrical noise measurements on the metallic phase of organic charge transfer salts.

The  measured noise spectrum is close to (but not exactly) 1/f.

The disparity of time/energy scales.
What is the relationship (if any) between the noise (which is sometimes measured on time scales as long as one thousand seconds (mHz)) and microscopics (which one might calculate with quantum chemistry and/or Hubbard models, but typically involves energies larger than meV or frequencies that can be ten orders of magnitude larger)?

Obscure trends.
If one looks at the actual exponent alpha of the noise, 1/f^alpha. It varies in a non-monotonic way as the temperature T varies. This looks rather "random" to me (i.e. I found it hard to believe there was any systematics involved).

However, Jens Muller and collaborators have used a model due to Dutta, Dimon, and Horn (DDH) to nicely elucidate what is going on in a series of papers such as this one.

Origin of the glass-like dynamics in molecular metals κ-(BEDT-TTF)2X: implications from fluctuation spectroscopy and ab initio calculations 
Jens Müller, Benedikt Hartmann, Robert Rommel, Jens Brandenburg, Stephen M Winter, and John A Schlueter

Here are the basic ideas of the DDH model.
There is a distribution of relaxation times tau, which arise because there are a distribution of activation energies E for relaxation.

tau0 is a typical "attempt frequency"/molecular vibration frequency for something like a conformational change of a molecule.

One assumes that for a specific tau that the noise is simply Lorentzian. But one then averages over D(E), the distribution of activation energies.

One can then show that at a given temperature the noise has a 1/f^alpha form with an exponent given by,

A specific consistency test of the model is to then compare the measured alpha to that calculated from the above expression using the observed temperature dependence of the noise spectrum. This comparison is shown in the figure above. 

One can also invert the equation above to extract D(E), giving the result in the figure below.

These two points give a better understanding of where the temperature dependence of alpha comes from; it has a reasonable explanation in terms of the distribution of activation energies.

Furthermore, the origin of the low frequency noise is the relatively large value of the activation energies. This leads to conformational transitions being extremely rare. In particular, I find it amazing that the noise at the Hz scale is detecting the fact that in the macroscopic crystal about every one second a single molecule (yes, just one undergoes a conformational change)!

Note that the activation energy distribution D(E) is peaked around 230 meV. This is the same energy that is deduced from studies of the activation energy for the glassy behaviour seen in NMR, specific heat, and thermal expansion. Moreover it is also the energy barrier calculated from quantum chemistry for the transition between the two conformations of the ethylene end groups (staggered vs. eclipsed) that I discussed in a recent post.

The reference given above also gives an explanation using ab initio calculations as to why the presence of the glass transition depends on the chemical identity of the anion X in kappa-(BEDT-TTF)2X. It relates to the relative strength of the bonding between X and the ethylene end groups of the BEDT-TTF molecules.

One thing that is not clear is what determines the width of the distribution D(E).

There are subtleties that I have glossed over here and other interesting things but the aim of this post is to focus on the big picture and some of my basic puzzles.

I thank Jens Muller for a very helpful discussion about his work.

Tutorial on bad metals

After yesterday's colloquium a large group of IISER students (both undergraduate and graduate) expressed an interest in having a tutorial on more of the subject of emergent quantum matter.
It is today at 6pm after they are done with the days lectures. This tells you something about the quality of the students and institution!

I am going to give a tutorial about bad metals. I will probably cover half of these slides. Hopefully there will be lots of questions and side discussions on the blackboard.

Emergent quantum matter talk at IISER Pune

On monday I am giving a talk at the Indian Institute for Science Education and Research (IISER ) Pune.
Here is the current version of the slides.

A minor detail that matters in organic charge transfer salts

One helpful way to think about condensed matter is in terms of relative energy scales. This can help one decide what is important and what is not.
However, this does not always work, particularly in complex systems where new low energy scales can emerge.

For a long time there has been a "minor detail" about organic charge transfer salts based on the BEDT-TTF molecule that I have found rather annoying and puzzling.
It concerns the role of ethylene end groups on the molecule and their possible different conformations (eclipsed vs. staggered).

Why should the conformations matter?

I would think not. The overlap of the relevant electronic molecular orbitals which are largely centred on sulphur atoms are negligible as seen below in the HOMO (Highest Occupied Molecular Orbital) for a BEDT-TTF dimer.

The figures are taken from this paper by Edan Scriven and Ben Powell.

However, things are more subtle than I would have thought.

Here are some of the significant effects that result from these two different conformations. They have different energies and by thermal annealing in a crystal you can convert between them.
As a result disorder in a crystal can be controlled by varying the cooling rate.
In some materials there is even a glass transition around 80 Kelvin.

Examples of the dramatic effects of the disorder can be seen.

Resistance vs. temperature curve (see for example the figure below taken from here).

Suppression of the superconducting transition temperature.
This can be seen in the curves above.

Electrical noise experiments

Another dramatic effect of the ethylene groups that is much larger than most people expect is
Isotopic substitution of the hydrogen with deuterium in the ethylene groups can drive the Mott metal-insulator transition. 
This somehow arises from a geometrical isotope effect associated with hydrogen bonds between the ethylene groups and the anion.

It turns out that changing the conformation of the end group can have a significant effect on the parameters in the Hubbard model, that is the simplest possible effective Hamiltonian for these materials.
This is shown in this recent paper which estimates these parameters using DFT-based electronic structure calculations and Wannier orbitals to map onto a tight-binding model.

Influence of molecular conformations on the electronic structure of organic charge transfer salts Daniel Guterding, Roser Valentí, and Harald O. Jeschke .

In particular in going from Eclipsed (E) to Staggered (S) or visa versa is enough to cross the Mott insulator-metal phase boundary.
This provides a framework to understand the experimental puzzles discussed above.

One minor quibble. 
The authors estimate the Hubbard paper U (Coulomb interaction) for two holes on a BEDT-TTF dimer with a formula which is only valid in a particular limit.
The general formula for the energy of  two electrons on a two site Hubbard model is

where Um is the Hubbard interaction on a single dimer, V is the inter site Coulomb repulsion and t is the intersite hopping. The authors are assuming that Um - Vm is much larger than 4t which Scriven and Powell argue is not the case.
This will lead to quantitative changes but not change the main point that the conformational changes can produce a significant change in the Hubbard model parameters; particularly a large enough change to cross the Mott insulator-metal phase boundary.

Later I will write about the noise measurements (which I puzzled about before) which turn out to be a very sensitive probe of these two molecular conformations and their interconversion.

I thank Jens Muller for very helpful discussions about this work.

SciPost is a great initiative towards restoring science to journals

"SciPost is a a complete scientific publication portal managed by active professional scientists."

It is worth checking out.
SciPost addresses many concerns I have about the current sorry state of science and publishing. These include that journals becoming redundant and counter productive and so we need alternative publication models, particularly not involving for-profit companies.

One thing I particularly like is the transparency. All the referee reports are public and referees have the option of being anonymous or not. Furthermore, anyone can write a report. Authors responses to the reports are also public.
I think this public accountability may raise standards significantly.

I hope you (and I) will consider supporting it by
-  submitting articles
- writing referee reports (either on request or volunteering)
- writing commentaries
- being willing to serve on the Editorial College

Jean-Sebastien Caux is to be commended for all the work he has put into this.
I thank Matt Davis for bringing this significant initiative to my attention.