Quenching the Kitaev honeycomb model

>> Ref 1, main point; and Ref 2-1: Discussion on prethermalization
Response: I think I finally find the origin of our misunderstanding, leading hopefully to convergence on our understanding of my results.
The ‘prethermal’ regime has two phenomenon that need to be explained:
1) Why does it take exponentially long in Jxy/Jz for the system to relax?
2) Why are there persistent magnetization oscillations in this regime?
In the renewed manuscript, I made this distinction clearer. The answer to the first question lays within the realm of prethermalization theory, in particular Ref. [23].
In the new manuscript, I elaborate more on the answer to the second question, which is largely inspired by the referee’s comments. Indeed, starting with an initial Neel state in the toric code, one would expect T=8Pi Jz^3/Jxy^4 periodic oscillations of the staggered magnetization. The essence of the prethermal regime is that the dynamics are * as if * the system is undergoing evolution with a toric code. Indeed, in the new Fig. 6, you can see that this is the case. When J_xy < 0.2 Jz, the oscillations follow almost perfectly the expectations from a toric code.
I hope that with this extension, the section 3.2 has become suitable for publication.

>> Ref 1, second point: "While I understand that potentially one can use all u_ij to encode the vortex sector, many of these encodings lead to the same physical scenario. It seems to me that the N_c \approx 2^3N number here seems to be a fairly significant ..."
Response: Actually, it is true that the gauge freedom allows you to construct the Néel state with maybe fewer gauge field configurations than I used. However, the construction I chose has the advantage of being very transparent in that it is a equal-weight superposition of all the possible configurations that satisfy the given criteria. I will add a comment along these lines to the new manuscript.

>> Ref 2-2: "There has been considerable discussion in the reports and response with regards to free fermions, etc. I believe that if the initial state chosen were the zero-flux sector, one could get away with an effectively free fermion treatment (since the Kitaev Hamiltonian conserves flux)?"
This is correct.
"But now, the novelty here is the initial Neel state, which has superpositions of different flux sectors, making the gauge coupling important."
Again, correct.
"The paper would benefit greatly from having a discussion on this point in connection to quenches, given the subtle discussions."
I will add a discussion on this at the end of Sec. 2.

>> Ref 2-3. " I think the specific choice of operators, i.e. S^z correlators, and perhaps the magnetization too, overcomes this problem in getting rid of the string in the Majorana basis? Could the author comment on this in the manuscript?"
If I understand the referee correctly, the point is that within my choice of Majorana-Gauge field basis, it is much simpler to compute Sz and correlators of Sz than Sx and Sy-expectation values. I will add a comment on this at the end of Sec. 2.