Thursday, June 3, 2021

A Myth about Condensed Matter Physics?

What is condensed matter physics about? 

In his beautiful book, The Problems of Physics (originally published in 1987), Leggett has a nice chapter about condensed matter physics, Physics on a human scale. The abstract begins:

This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level components is a myth, and that the analogy of map-making is much more appropriate.

Here are some quotes that clarify Leggett's argument.

a number of cases, particularly in the traditional areas of the physics of gases and crystalline solids, in which a model which treats the behaviour of the whole as essentially just the sum of that of its parts (atoms or electrons) has been quite successful; and a few more in which, even if a ‘one- particle’ picture fails, a description in terms of pairs of particles interacting in a way which is not particularly sensitive to the environment gives good results. But these cases, despite the fact that they totally dominate the presentation of the subject in most elementary textbooks, are actually the exception rather than the rule. 

In virtually all the frontier areas of modern condensed-matter physics, the relationship between our understanding of the behaviour of matter at the microscopic level of single atoms and electrons, and at the macroscopic level of (say) liquids and solids, is actually a good deal more complicated than this.

If the activity just described is not what condensed-matter physics is all about, then what is it about? I would claim that the most important advances in this area come about by the emergence of qualitatively new concepts at the intermediate or macroscopic levels—concepts which, one hopes, will be compatible with one's information about the microscopic constituents, but which are in no sense logically dependent on it. 

... [these new concepts] provide a new way of classifying a seemingly intractable mass of information, of selecting the important variables from the innumerable possible variables which one can identify in a macroscopic system;

All this is not to deny that an important role is played in condensed-matter physics by attempts to relate the macroscopic behaviour of bulk matter to our knowledge concerning its constituent atoms and electrons. Indeed, the theoretical literature on the subject is full of papers which at first sight seem to be claiming to ‘derive’ the former from the latter—that is, to do exactly what I have just said condensed-matter physicists do not do. 

It is precisely this compelling need to isolate, from a vast and initially undifferentiated mass of information, the features which are relevant to the questions one wishes to ask, which distinguishes condensed-matter physics qualitatively from areas such as atomic or particle physics...

In this situation I believe that it is sensible to reorient our view of the kinds of questions that we are really asking in condensed-matter physics. Rather than chasing after the almost certainly chimerical goal of deducing the behaviour of macroscopic bodies rigorously from postulates regarding the microscopic level, it may be better to view the main point of the discipline as, first, the building of autonomous concepts or models at various levels, ranging all the way from the level of atomic and subatomic physics to that of thermodynamics; and, second, the demonstration that the relation between these models at various levels is one not of deducibility but of consistency—that is, that there are indeed ‘physical approximations’ we can make which make the models at various levels mutually compatible.

In different words, condensed matter physics is all about emergence! [Although, I know Leggett does not like the way the word is used]. 

The centrality of intermediate scales was also emphasised by Tom McLeish in Soft Matter: A Very Short Introduction.

When I recently read Leggett's chapter I was concerned that this might be in conflict with my draft manuscript of Condensed Matter Physics: A Very Short Introduction.  In the first chapter, I wrote the following.

The central question of Condensed Matter Physics

Generally, condensed matter physicists grapple with one question. Because it is so important I state the question in three different ways.

How do macroscopic properties emerge from microscopic properties? 

How do the properties of a state of matter emerge from the properties of the atoms in the material and the interactions between the atoms?

How do the many atoms in a material interact with one another to collectively produce a particular property of the material? 

I think this is consistent with Leggett's perspective, particularly because I do later emphasise emergence and intermediate scales. On the other hand, I may not have the same emphasis (or strong language) that Leggett does. 

Leggett's view is particularly pertinent today because a quarter of a century later there are probably a lot more people who would say that they are condensed matter physicists but would subscribe to the "myth". This is because of the rise of computational materials science due to massive increases in computational power and better computational methods such as those based on Density Functional Theory (DFT), using "better" functionals and DMFT (Dynamical Mean-Field Theory).

What do you think?

1 comment:

  1. https://unherd.com/2021/06/beijings-useful-idiots/

    Ian Birell's take on Lancet and Nature journals.

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