In the Hatsugai-Kohmoto model, Fermi surface topology transitions quantified by Fermi sea volume and Euler characteristic unify metal-insulator and Lifshitz transitions under a robust universality class, with gapless phases identified as Landau Fermi liquids.
Qualitatively, the analysis below bears on some resemblance between the 1dHK model and the fermionic ladder dealt with earlier in [1]
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Topology of the Fermi surface and universality of the metal-metal and metal-insulator transitions: $d$-dimensional Hatsugai-Kohmoto model as an example
In the Hatsugai-Kohmoto model, Fermi surface topology transitions quantified by Fermi sea volume and Euler characteristic unify metal-insulator and Lifshitz transitions under a robust universality class, with gapless phases identified as Landau Fermi liquids.