Saturday, July 21, 2018

Questions about slave-particle mean-field theories of Hund's metals

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 captured by slave-boson mean-field theory, including the small coherence temperature.

In contrast, to a "Mott metal", a Hund's metal is associated with suppression of singlet spin fluctuations on different orbitals, without suppression of charge fluctuations and is seen in a Z_2 slave-spin mean-field theory at zero temperature.

Specific questions are whether slave mean-field theories at finite temperature can capture the following?
  • The coherence temperature, T*.
  • A suppression of spin singlet fluctuations at T increases towards T*.
  • An orbital-selective bad metal may occur in proximity to an orbital selective Mott transition. This is where at least one band (orbital) is a Fermi liquid and another is a bad metal. This would mean that there are two different coherence temperatures. 
  • The emergence of a single low-energy scale, common in both bands, as is seen in DMFT.
  • The spin-freezing temperature.
Finally, how does the stability of the Hund's metal change with the number of orbitals?
Figures in this post suggest that the Hund's physics is more pronounced with increasing the number of orbitals. However, that may be because the critical U (and thus proximity to the Mott insulator) changes with the number of orbitals and all the curves are for the same U.

Thursday, July 19, 2018

It's not complicated. It's Complex!

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, economics, and sociology are examples of CAS.

The book gives a rather dense (but worthwhile) introduction to key concepts in complexity theory including the emergence of specialists (e.g., division of labor, according to Adam Smith in economics), the role of diversity, co-evolution (e.g. Darwin's orchid and moth), and evolutionary niches (fixed points of Markov matrices!).

Holland smoothly flits backwards and forwards between examples in biology, economics, linguistics, and computer science.

Holland's definition of emergence is consistent with how I think in condensed matter. For example, the formation of weakly interacting quasi-particles in a Fermi liquid. The emergent "boundaries" define the spatial size of the quasi-particle.
What struck me is that the interactions should be viewed as emergent, just as much as the quasi-particles.
For example, if we start with quarks and QCD (quantum chromodynamics), then at "low" temperatures and densities, nucleons form and the nuclear force emerges.

Tuesday, July 17, 2018

How do you get in a productive zone?

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 loud music!

Some people function well with deadlines. Others crumble under the pressure. Some work well with short bursts during the day. Others need to block out a day or even a week to focus on something.

Involvement of others.
Some people will work best alone on a task, with minimal interactions with others. Others will barely function without input and feedback from others at many points in the process.

Good managers are sensitive to this diversity of needs and will aim to provide the appropriate environment for different individuals.

This post was stimulated by a recent experience how something came together and I was able to get a lot of work done on a specific task during a couple of plane flights. This seemed a bit random because these days I rarely work on flights because it is really non-productive.

What do you think?
What helps you get in the right "zone"?

Sunday, July 8, 2018

Square ice on graphene?

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 GroƟ

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 bounded by two layers of graphene.

The figure below summarises the authors results for free-standing layers showing how the relative stability of the different water structures depends on the area density of water molecules [which varies the length and strength of the hydrogen bonds].

On the science side, there are several interesting questions arise.
How much do the results depend on the choice of DFT functional used [RPBE with dispersion corrections]?
Would inclusion of the nuclear zero-point energy modify the relative stability of some of the structures, as it does for the water hexamer?
Quantum nuclear effects are particularly important when the hydrogen bond length [distance between oxygen atoms] is about 2.4 Angstroms. [I am not quite sure what area density this corresponds to for the different structures].

On the sociology side, this paper is another example of a distressingly common progression:
1. A paper in a luxury journal reports an exotic and exciting new result.
2. More papers appear, some supporting and some raising questions about the result.
3. A very careful analysis reported in a solid professional journal shows the original claim was largely wrong. This paper attracts few citations because the community has moved on to the latest exciting new "discovery" reported in a luxury journal.

I thank Tanglaw Roman for helpful discussions about his paper.

Saturday, June 23, 2018

The discipline of defining good research questions

I have a friend who works in a small college that offers Masters degrees in the humanities. In one program each student must do a thesis on a research topic over the course of a year. My friend spends a lot of time with the students, both individually and as a group, posing and refining a single question for each of their research projects. Last year while visiting I observed one of these sessions and also to have some discussions with individual students about their questions.

The stages are roughly this.

1. The student picks a specific research topic.
2. The student proposes a specific question about the topic that they will aim to answer.
3. The student meets with their advisor to refine the question. Often this involves making it more specific and narrow so that it is manageable.
4. The student presents their question to the class (often about five students) who then discuss it and try and refine it further.
5. With this feedback the student again refines it.
6. The student meets their advisor for a final discussion and agreement about the question.
7. The student starts research.

The questions can start with How, What, When, or Why?
Often, Why is preferred, because it may mean going deeper.

Several things struck me about this practise, particularly seeing it first hand.
First, how valuable it was in terms of ending up with questions that were more interesting, precise, valuable, and manageable.
Second, how valuable this was for the students in terms of learning to think more critically.
Third, how little I think we do this in science.

I don't think the key thing here is that it is a humanities practise. Rather, I think it is that the complete ethos of the college is teaching and training students.

My experience is that we tend to just pick topics for students and suggest they measure or calculate something and see what happens. We may mention a question but we don't refine it or keep coming back to it. Similar concerns apply to many grant applications. It is often not clear whether they are really aiming to provide definitive answers to any questions. I think that there are two big obstacles to us following this procedure: it is hard work and the "publish or perish" culture.

Some of this relates to the challenges of falsifiability and the method of multiple alternative hypotheses.

One (maybe) obvious caveat. Although one starts with this question, as the research proceeds, one may choose to or need to modify the question as one learns more.

What do you think?
Is this something we could be doing better?

Tuesday, June 19, 2018

Different phases of growth and change in human organisations

When reflecting on the current state of an organisation (whether a university, a research group, an NGO, a funding agency, a state government department, a business, ...) it is natural to consider two questions.

How did it get to where it is today? In particular, what is the origin of its current positive and negative properties?

What can be done to move it in a positive direction in the future?

Human organisations are complex and diverse, yet their evolution as they grow seem to exhibit certain universal features, that transcend both the purpose and the relative size of the organisation.
There is a classic article, Evolution and Revolution as Organizations, by Larry E. Greiner, originally published by the Harvard Business Review in 1972.

The article is summarised in the figure below.

Greiner was solely concerned with businesses. However, this model has since been applied to other types of organisations.
Aside: His article contains no data or references! Perhaps, his excuse is that he wrote the article in a Swiss ski resort (long before the internet) while recovering from a skiing injury!

I will illustrate the model by considering how it might describe the evolution of a scientific research group. It starts with a young faculty member and ends being part of a large research institute.

Phase 1: Creativity.
A young assistant professor (PI) starts a new research group with start-up funds and two graduate students. They are attracted to work with her because of her passion and the excitement of working on a new technique from the ground up. Lots of different things are tried to get the technique to work. Indeed the original technique does not work but a new one is discovered. Everyone works long hours in the lab. The future is uncertain. She may not get funding or tenure. There is frequent and informal communication within the group. Thus, there is really no need for formal group meetings or policies. After about five years things start to change. Papers are published. Grant applications are successful. More grad students and a postdoc join the group. Tenure is granted. But some frustrations grow as the informality no longer works. The leader spends less time in the lab, travels more, and is less available to students. This leads to the next phase.

Phase 2: Direction.
There is a need for consolidation and organisation. The new technique is now well established. The goal is now to use it as much as possible on a suite of materials. The focus is on fine tuning the technique not on making big new discoveries. Creativity is valued less. There are now weekly group meetings. Each student has a weekly meeting with the PI. Communication becomes more formal and the relationships more distant. The group is now producing a steady stream of papers attracting more grants, and is now joined by undergraduates, visiting faculty, and more grad students and postdocs. There are now formal policies about lab use. People now join the group for different reasons than before. Some are attracted by stability or reputation. Frustrations are present and conflicts associated with competition for resources, whether concerning access to instruments, time with the PI, or author order on papers. The success of the group leads to it attracting more resources. But, this comes with the cost of increased accountability and the associated administrative load. The PI now spends more time communicating with funding agencies, university management, and collaborators, than with people in the group. The PI is rarely seen in the lab, and enjoys her job less.

Phase 3: Delegation.
The PI now delegates supervision of graduate students to postdocs. A technical officer is hired to manage the lab. A group secretary (or PA) takes care of many administrative matters and schedules meetings between group members and the PI. A theory postdoc is hired to do in-house theory. The department hires a new junior faculty member to work in a research area that has some overlap with this well-established group. As the group grows into new areas it becomes divided by research topic or technique. Competition between sub-groups emerge for resources and attention. The PI has lost control over the whole operation and there is a lack of co-ordination between sub-groups.

Phase 4: Co-ordination.
Part of the research group moves into new labs in a new institute building on campus, with a newly hired director. He works with his business manager to impose co-ordination between research groups. The original PI often receives attractive job offers and finally moves to a different university, partly in frustration. The institute director uses this as an opportunity to "reorganise" the different groups in the institute with the goal to make them co-ordinate better about use of instruments, grant applications, and collaborations. He also puts pressure on each group to be self-sustaining financially.
Things have now become quite impersonal and bureaucratic. Some graduate students now join the group because they are impressed by the shiny new building and all the expensive instruments in the lab. But some, older graduate students and postdocs resent the "managers" who they consider have little experience at the "coal face" of research. There is not much innovation or creativity happening. This all leads to the "red-tape" crisis.

Phase 5: Collaboration.
Greiner claims:
The last observable phase emphasizes strong interpersonal collaboration in an attempt to overcome the red-tape crisis. Where Phase 4 was managed through formal systems and procedures, Phase 5 emphasizes spontaneity in management action through teams and the skillful confrontation of interpersonal differences. Social control and self-discipline replace formal control. This transition is especially difficult for the experts who created the coordination systems as well as for the line managers who relied on formal methods for answers.
I remain to be convinced whether this actually ever happens. It is certainly what is desirable, but the obstacles to it happening seem formidable.

Greiner claims that each phase of growth produces problems that lead to a revolution.
But, in each phase of growth the solutions implemented in the previous revolution inevitably produce problems that lead to a new crisis and revolution.
Ironically, for a business professor this determinist perspective (inevitability) is a somewhat Marxist view of history!

A second important claim is that the type of managers or leaders required at the different phases have quite different personalities, strengths, skills, values, and training. Consequently, each revolution is associated with a time of conflict within the organisation.

Why am I interested in all of this? How is it relevant to universities?
There are two ideas that I think are particularly important.

The first idea, is that different phases of growth attract quite different types of people to the organisation. The first phase tends to attract creative people who are driven by passion for thinking, learning, and research. They are independent thinkers who tend to dislike formality and structure.
In contrast, success and growth leads to attracting people who may be more motivated by money, power, or social status. Furthermore, they may be more passionate about organisation, procedures, and structures, than the actual original "core business." In fact, they would be just as happy working in HR, finance, or management in a soft drinks company, a large NGO, as in a university. These differences inevitably lead to conflicts of values. I think this is actually one of the major problems of research universities today. They have become so "successful", large, wealthy, and complex, that they now attract the "wrong" type of people to leadership and management. Passion for transformative education of undergraduates and for creative diligent scholarship is just not present.

The second idea, is the incredible challenge of going from phase 4 to phase 5. In a complex and large organisation how do you create a culture and structures that use the massive resources of the large organisation to actually foster the creativity, entrepreneurship, flexibility, and passion of "grass roots" activities that were present at stage 1, and are essential for the long-term viability and relevance of the organisation.

What do think about Greiner's growth model?
How is it relevant, whether to research groups, departments, or universities?

Friday, June 15, 2018

Quantum spin liquid on the hyper-honeycomb lattice

Two of my UQ colleagues have a nice preprint that brings together many fascinating subjects including strong electron correlations and MOFs. Again it highlights an ongoing theme of this blog, how chemically complex materials can exhibit interesting physics. A great appeal of MOFs is the possibility of using chemical "tuneability" to design materials with specific physical properties.

A theory of the quantum spin liquid in the hyper-honeycomb metal-organic framework [(C2H5)3NH]2Cu2(C2O4)3 from first principles 
A. C. Jacko, B. J. Powell

What is a hyper-honeycomb lattice?
It is a three-dimensional version of the honeycomb lattice.
A simple tight-binding model on the lattice has Dirac cones, just like graphene.

The preprint is a nice example how one can start with a structure that is chemically and structurally complex and then use calculations based on Density Functional Theory (DFT) to derive a "simple" effective Hamiltonian (in this case an antiferrromagnetic Heisenberg model of coupled chains) to describe the low-energy physics of the material.
We construct a tight-binding model of [(C2H5)3NH]2Cu2(C2O4)3 from Wannier orbital overlaps. Including interactions within the Jahn-Teller distorted Cu-centered eg Wannier orbitals leads to an effective Heisenberg model. The hyper-honeycomb lattice contains two symmetry distinct sublattices of Cu atoms arranged in coupled chains. One sublattice is strongly dimerized, the other forms isotropic antiferromagnetic chains. Integrating out the strongest (intradimer) exchange interactions leaves extremely weakly coupled Heisenberg chains, consistent with the observed low temperature physics.
There is some rather subtle physics involved in the superexchange processes that determine the magnitude of the antiferromagnetic interactions J between neighbouring spins. In particular, there are destructive quantum interference effects that reduce one of the J's by an order of magnitude and increases another by an order of magnitude. To illustrate this effect, the authors also evaluate the J's when one flips the sign of some of the matrix elements in the tight-binding model. Similar subtle physics has also been observed in different families of organic charge transfer salts.

As an aside, there is some similarity (albeit many differences) with the basic chemistry of the insulating phase of cuprates: the parent compound involves a lattice of copper ions (d9) where there are three electrons in eg orbitals that are split by a Jahn-Teller distortion. The differences here are first, that the interactions between the frontier orbitals on the Cu sites is not via virtual processes involving oxygen p-orbitals but rather via pi-orbitals on the oxalate bridging orbitals. Second, the lattice of Cu orbitals is not a square but the hyper-honeycomb lattice.

The preprint is motivated by a recent experimental paper in JACS
Quantum Spin Liquid from a Three-Dimensional Copper-Oxalate Framework 
Bin Zhang, Peter J. Baker, Yan Zhang, Dongwei Wang, Zheming Wang, Shaokui Su, Daoben Zhu, and Francis L. Pratt