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Quantum robustness and phase transitions of the 3D Toric Code in a field

by D. A. Reiss, K. P. Schmidt

This Submission thread is now published as

Submission summary

Authors (as Contributors): Kai Phillip Schmidt
Submission information
Arxiv Link: (pdf)
Date accepted: 2019-06-03
Date submitted: 2019-05-28 02:00
Submitted by: Schmidt, Kai Phillip
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study the robustness of 3D intrinsic topogical order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations reveal a ground-state phase diagram with first and second-order quantum phase transitions. The variational approach can be applied without further approximations only for certain field directions. In the general field case, an approximative scheme based on an expansion of the variational energy in orders of the variational parameters is developed. For the breakdown of the 3D intrinsic topological order, it is found that the (im-)mobility of the quasiparticle excitations is crucial in contrast to their fractional statistics.

Published as SciPost Phys. 6, 078 (2019)

Author comments upon resubmission

We thank the referee for carefully examining our article and for the overall
very positive comments on our work. In the revised version, we have addressed
the minor issues raised in the referee report and we have added one more reference.

List of changes

In the revised version of our article, we have addressed the following minor issues raised in the referee's report:

1) In the revised version we have explained Eq. 6 in more detail.
2) We have updated Eq. 8 according to the referees suggestions.
3) We have updated Eq. 9 according to the referees suggestions.
4) Here we do not agree with the referee. Our statement is not only valid in the loop-soup picture of the ground state. So we have left the formulation as it is.
5) We agree and we have "n_x \in Z" as suggested by the referee.
6) We agree and we haved added the commas as suggested by the referee.
7) We agree with the referee and updated the formula.
8) The factor 1/(2j) in Eq. 19 has been put inside the sum. We corrected this.
9) We have added a footnote on page 15 to explain this symbol.
10) We have followed the referee and changed the expressions on page 19.

Additionally, we added on page 17 the reference
M.H. Zarei, Physical Review B 96, 165146 (2019).
for the dual Hamiltonian of the 3D TFIM.

Submission & Refereeing History

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Resubmission 1902.03908v2 on 28 May 2019

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