Short version of my question is this : what is the nature of the phase transition in the Kitaev honeycomb model ?

Longer version:

Kitaev honeycomb model undergoes a phase transition from a gapped to a gapless-single-mode phase when the coupling constants are tuned. This way of describing the phases and the transition between them is different from the way classical thermal phase transitions are described, where one talks about order parameters, diverging correlation lengths and scale invariant critical theory (if it is a continuous transition), ergodicity breaking etc. Are there similar notions in the case of the Kitaev model ?

In the case of another phase transition in a quantum system, namely the transverse field Ising model (TFIM), I can define an order parameter (spin expectation value in a suitable direction). Since there is this order parameter, and a relevant tuning parameter (say the transverse field strength) I can think of quantum fluctuations of the order parameter, scaling of various correlations under tuning of the parameter etc in a manner similar to the classical transitions.

  • $\begingroup$ Have you seen the book by Subir Sachdev? There is also a Wikipedia article on quantum phase transitions that has a brief description and a few more references. $\endgroup$ – Stephen Powell Jan 26 '16 at 8:51
  • $\begingroup$ @StephenPowell, I have rewritten the text to explain my specific question. $\endgroup$ – symanzik138 Jan 28 '16 at 17:02
  • $\begingroup$ Thanks for clarifying. You should probably add "Kitaev honeycomb model" to the title. $\endgroup$ – Stephen Powell Feb 1 '16 at 10:45
  • $\begingroup$ I guess its a metal insulator type transition. If that is the case, a local order parameter is not known, I think. $\endgroup$ – symanzik138 Apr 4 '16 at 13:58
  • $\begingroup$ In this review by Savary and Balents, there's a remark on page 16 saying "[In] the toric code with an applied field [...], the critical properties are described by a simple scalar field theory, implying a 2+1 dimensional Ising universality class." It may be that the same is true for the honeycomb model, or that the same logic can be applied. There's a reference to Bais and Slingerland, but I don't have time at the moment to look at it carefully (which is why this is a comment, rather than an answer). $\endgroup$ – Stephen Powell May 4 '16 at 7:49

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