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Gauging the Kitaev chain
by Umberto Borla, Ruben Verresen, Jeet Shah, Sergej Moroz
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Submission summary
| Authors (as registered SciPost users): | Umberto Borla · Sergej Moroz · Ruben Verresen |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2010.00607v3 (pdf) |
| Date accepted: | 2021-05-27 |
| Date submitted: | 2021-05-21 17:52 |
| Submitted by: | Borla, Umberto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.
Author comments upon resubmission
We are grateful to both Referees for reading our paper and providing valuable feedback. In two replies we provide point-by-point answers to the comments of the Referees and the list of changes implemented in the present resubmission.
Best regards,
Umberto Borla, Ruben Verresen, Jeet Shah, Sergej Moroz
List of changes
- References: added references 34-37.
- Figures: expanded the caption to Fig. 3
-Figures: in the caption of Fig.5, we now explicitly refer to Fig.4 and Fig.6 for smaller/larger values of h, respectively.
- Section 1: Modified a sentence to “In particular, after gauging, the trivial phase of the Kitaev chain becomes a deconfined phase which for a positive chemical potential is stable to vortices, despite matter being massive, due to spontaneous translation symmetry-breaking giving rise to deconfined domain walls.”
- Section 2: we added the hermiticity condition of $\tilde \gamma$.
-Section 3.2: Added the sentence “Moreover, let us mention that although the case h = 0 can mapped to a free-fermion problem, this requires a non-local mapping which can obscure some of the relevant physics, so we do not follow this route.”
-Section 3.2: Added the sentence: “We stress that although the $h$-term in Eq.(14) was motivated by fixing a gauge on temporal links, the term itself is manifestly gauge-invariant in this quantum lattice gauge theory - indeed, it commutes with the gauge constraint in Eq.(15). ”
- Section 3.4: Added the sentence "Similar to those encountered in higher-dimensional gauge theories, such emergent fermions can only be created in pairs, consistent with the fact that any local operator in the bulk of this theory is bosonic."
Published as SciPost Phys. 10, 148 (2021)
Reports on this Submission
Report 2 by Paul Fendley on 2021-5-25 (Invited Report)
Report
The changes are fine, and I recommend publication in SciPost.