Is there any interacting fermionic model (i.e. with more than quadratic terms) which can be analytically diagonalised? Even the "simple looking" Hubbard model seems to lack an analytical solution. If no, is it even possible to diagonalise an interacting (fermionic) theory?

I'm asking this from a condensed matter perspective but other points of view are more than welcomed (HEP...etc).

  • 3
    $\begingroup$ It depends on your standards of "analytically diagonalized". But any Bethe ansatz (or otherwise) solvable spin model can be mapped to a fermionic model via a Jordan-Wigner transformation which is not necessarily non-interacting. (Take, e.g., the Heisenberg model, which maps to a Hubbard-type model.) $\endgroup$ Jul 21 at 14:42
  • $\begingroup$ @NorbertSchuch I only know the XY Heisenberg model mapping to free fermions via JW transform. I will look the Hubbard model one, thanks $\endgroup$ Jul 21 at 14:59
  • $\begingroup$ You can apply the inverse JW to any spin model with a Z2 symmetry. $\endgroup$ Jul 21 at 15:15
  • 3
    $\begingroup$ en.wikipedia.org/wiki/Thirring_model $\endgroup$ Jul 21 at 15:20
  • $\begingroup$ SYK? rational CFTs? $\endgroup$ Jul 24 at 7:57

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