Ideas in Condensed Matter Physics

Doug Natelson has a post soliciting suggestions for the most powerful idea in condensed matter physics, putting out the Hohenberg-Kohn-Sham theorem/method underlying DFT as being a good candidate. Others have suggested Bloch’s theorem, Anderson’s paper on localization, Laughlin’s paper on the Fractional Quantum Hall Effect, Onsager’s solution of the 2D Ising model, Landau’s papers on Fermi liquids, BCS theory, “and whatever the most appropriate Bethe ansatz paper is”.

I need to learn way more condensed matter physics in order to say anything constructive, although I do feel that another on the list could be Philip Anderson’s “More is Different: Broken symmetry and the nature of the hierarchichal structure of science“, which arguably set the tone for the principle (paradigm?) of emergence in complex systems (and perhaps unwillingly led to a good deal of philosophy and/or pseudoscience, too). Perhaps one of the most-quoted passages from the paper - that I’ve seen, at any rate - is the following:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe… The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.

Anyway, the post reminded me of a paper I came across a long time ago in Rev. Mod. Phys. by W. Kohn (of Hohenberg-Kohn-Sham, as mentioned above) in 1999 that basically attempts to document the evolution of condensed matter physics. Here’s an excerpt:

It is perhaps interesting to look at the history of condensed matter physics from the viewpoint of T. S. Kuhn… [who] sees scientific history as a succession of (1) periods of ‘‘normal’’ science, governed by serviceable scientific paradigms, followed by (2) transitional, troubled periods in which existing paradigms are found to be seriously wanting, which in turn lead to (3) ‘‘scientific revolutions,’’ i.e., the establishment of new paradigms, which may or may not be accompanied by the rejection of the old ones.

Such a linear view seems applicable to the whole field of CMP for some of the broadest revolutions, which directly or indirectly affected a large fraction of the field:

• x-ray diagnostics yielding crystal structures (1910s);
• achievement of low temperatures allowing the observation of calmed condensed matter (1900s);
• quantum mechanics, (1920s);
• the band-structure paradigm (1920s, 1930s);
• nuclear and electron spin magnetic-resonance diagnostics (1940s and 50s);
• neutron elastic and inelastic diagnostics (1950s);
• many-body electron theories (beginning in the 1930s, with major revolutionary steps in the 1950s and 60s);
• electronic computer-assisted theory and experiments (1960s-);
• soft matter (1960s-);
• and nanoscience (1980s-).

I like it - clearly this is very broad, but it’s a very good summary of how the field has evolved into what it is today.