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Consider a random, all to all, complex fermion hopping model on $N$ sites with quenched (Gaussian) disorder, that has a well defined large $N$ limit (aka the SYK2 model). So, we start with free fermions in this model and after disorder averaging we lose the quasiparticles in this model. Is there a nice physical way to understand this result? Or should this simply be taken as a mathematical consequence of the Schwinger Dyson equations and that's all there is to it?

Example/Reference: Look at equation A3 on page 25 in this paper.

Qmechanic
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Vivek
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  • Are you sure we lose quasiparticles? After averaging which quantities? – fqq Apr 17 '20 at 17:08
  • After averaging over the Gaussian disorder. For instance, consider the disorder averaged single particle Green function: the Schwinger Dyson in this case is simply $\Sigma(\tau) \propto G(\tau)$, where $G(\tau)$ is the renormalized Green function, which eliminates the pole in single particle Green function. – Vivek Apr 17 '20 at 17:12
  • I think a handwaving explanation is that the low-energy spectrum is dominated Goldstone modes from spontaneously breaking down to $SL(2, \mathbf{R})$ symmetry (that pick up a small mass due to explicit symmetry breaking). – d_b Apr 17 '20 at 20:01
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    @d_b Umm, not sure, how would one argue that the breaking of the emergent reparametrization & gauge symmetry should make the quasiparticles vanish? For instance, in neutral superfluids, breaking of the global gauge symmetry and considering Goldstone mode fluctuations in phase still retains the Bogoliubov quasiparticles (they are massless but there)... – Vivek Apr 17 '20 at 20:27
  • In contrast to your statement, the paper appears to say (near the top of p.5) that for $q=2$, that is the random hopping case which is calculated in eq. (A3), the SYK model has Fermi liquid behavior and quasiparticles at low temperature. Am I misunderstanding your question? – Rococo Apr 18 '20 at 22:31
  • The first sections of this thesis give a nice introduction to the SYK model, which also appears to be consistent with this understanding: http://qpt.physics.harvard.edu/theses/Wenbo_Fu_thesis.pdf – Rococo Apr 18 '20 at 22:32
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    @Rococo Thanks. Indeed, that's what they always say. It's in Sachdev's papers, talks and Wenbo Fu's thesis as well. But if I look at the retarded Green function of SYK2 (in frequency domain), I can't find a zero of the denominator, let alone a pole. Could I be missing something? – Vivek Apr 19 '20 at 17:06
  • Thanks! I understand your question now. – Rococo Apr 20 '20 at 14:03

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