tag:blogger.com,1999:blog-13869903.post4427379692935303173..comments2024-03-28T04:15:44.459-05:00Comments on nanoscale views: The Orthogonality Catastrophe (!)Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-13869903.post-83952511127246134652013-11-13T21:21:11.844-06:002013-11-13T21:21:11.844-06:00I prefer overly understated language myself. E.g.,...I prefer overly understated language myself. E.g., "Absence of Diffusion in Certain Random Lattices," Anderson's 1958 breakthrough paper on localization. Or, "Infinite conformal symmetry in two-dimensional quantum field theory," (BPZ) as opposed to, say, "Exact solution to (almost all) 2D critical phenomena," or "One (Virasoro) algebra to rule them all."<br /><br />As for topological surface states, I'm happy with robust to disorder OR (sufficiently weak) interactions. The precise statement with respect to disorder is not the the prediction of vanishing linewidth, but the absence of localization in the presence of disorder. A finite lifetime just means inelastic scattering. For interactions, the robustness is the absence of an interaction-induced (i.e. Mott) gap. However, the combination of disorder and interactions can be deadly...Matthew Fosterhttps://www.blogger.com/profile/17461175352564741190noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-65442420059284754602013-11-13T20:46:46.896-06:002013-11-13T20:46:46.896-06:00This comment has been removed by the author.Matthew Fosterhttps://www.blogger.com/profile/17461175352564741190noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-26648932544772586412013-11-13T20:20:00.818-06:002013-11-13T20:20:00.818-06:00What about the polar catastrophe?
In the end it i...What about the polar catastrophe?<br /><br />In the end it is an avoided event (that being a deliberate choice of words). <br />One could even say it's "just" an electronic reconstruction.<br /><br />Another example is not from the negative dramatic side, but from the positive side: the "robustness" of surface states on topological insulators against disorder.<br />THey are robust against backscattering (because of time reversal symmetry), and there will be a conductive state because of the change in topological invariant. But robust against disorder is overdone - see what you see (ARPES E(k)) in a surface exposed to air. The state definitely changes width, and thus lifetime. So robust is too much.<br /><br />Anyway, these are two of my pet-peeves :-)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-6405887981138434462013-11-13T04:52:03.754-06:002013-11-13T04:52:03.754-06:00Basically it is the physics of recoil. Through int...Basically it is the physics of recoil. Through interaction with the Fermi sea, the added particle can excite particle hole pairs. In general, these may be have arbitrarily low energies (i.e. hole just below the Fermi surface and particle just above) but finite momentum (because the momentum of particle and hole can point in different directions). <br /><br />By momentum conservation, the balance of momentum must be taken up by the injected particle, and if its mass is finite, the resulting kinetic energy sets an energy scale p_F^2/2M. Below this scale particle hole pairs can't be excited -- or rather the phase space volume for doing so is dramatically reduced because then the directions of the momentum of particle and hole must almost coincide.<br /><br />If you consider the heavy limit M to infinity, you get a true IR catastrophe. Likewise in 1D, because the momenta are pointing in the same direction anyway.<br /><br />A nice discussion of the effects of recoil in different dimension is Nozieres, J. Phys. I France 4 (1994) 1275-1280.<br /><br />The survival of orthogonality catastrophe for massive impurities in 1D is the main piece of physics behind the "beyond Luttinger liquid" theories reviewed in Adilet et al. Rev. Mod. Phys. 84, 1253–1306 (2012)Austenhttps://www.blogger.com/profile/05639020827408234405noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-59235067709024994352013-11-12T09:55:43.862-06:002013-11-12T09:55:43.862-06:00Hi Austen - Thanks for the insightful comment. Th...Hi Austen - Thanks for the insightful comment. This is something that I'd like to understand better. Is there an intuitive way to understand the cases you mention? Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-61323118807021267232013-11-12T08:56:56.987-06:002013-11-12T08:56:56.987-06:00The curious thing about the orthogonality catastro...The curious thing about the orthogonality catastrophe is that it turns out to be much less important in many-body physics than the generality of the above argument suggests. <br /><br />For example, the quasiparticle weight Z (i.e. the residue of the single particle Green's function) is a measure of the overlap of the true ground state with the product state of a free particle and the ground state with one fewer particle. The orthogonality argument would suggest that Z is generically zero, while in fact finite values are the norm. 1D (i.e. in a Luttinger liquid) and the case of adding an infinite mass particle (heavy hole, in the original papers) are two of the situations where you really do get zero. PWA made numerous efforts to argue that the same happens in 2D to substantiate exotic theories of high Tc, to no avail.Austenhttps://www.blogger.com/profile/05639020827408234405noreply@blogger.com