What is the Kitaev Model and why has it become so popular? I am seeing Kitaev Model everywhere. It feels like the spin-glass model of our time. How the Kitaev model differ from spin-glass and why it can be used everywhere? Looking at equation 1 here suggests it's basically a spin-glass model.
 A: The paper linked in the original post already answers some of the post's questions.


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*What is the Kitaev Model?
It's a lattice model where

nearest  neighbor spin degrees of freedom interact via a strongly anisotropic nearest-neighbor Ising exchange [...] The Kitaev interactions along neighboring bonds cannot be satisfied simultaneously, giving rise to ‘exchange frustration’ and driving the system into a Quantum spin liquid (QSL) phase.



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*Why it became so popular?

The Kitaev honeycomb model is arguably the paradigmatic example of QSL, because of its unique combination of being experimentally relevant, exactly solvable and hosting a variety of different interesting gapped and gapless QSL phases, not the least a chiral QSL that harbors nonabelian Ising anyons



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*How the Kitaev model differ from spin-glass?
Spin glasses exhibit static, frozen ground states and meta-stable states, while in quantum spin liquids

the spins fluctuate strongly even at zero temperature.

Or, as more explicitly put by Perreault in his PhD. dissertation,

These two states are particularly distinguished by
  their dynamics since a spin glass has a very long single-spin autocorrelation time while a spin-liquid lacks such frozen spin configurations.

One could then ask which characteristic of the model (or material) allows for QSL. According to Balents' paper (e-print) a possibility is systems where

quantum effects are strong, and there are no obvious energy barriers [between low-temperature configurations].



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*Why it can be used everywhere?
It probably can't, but it's analytically solvable, which is a rare beast, so people are gonna apply it whenever possible and try to squeeze as much as possible from it.
