# Gauging the Kitaev chain

### Submission summary

 As Contributors: Umberto Borla · Sergej Moroz Arxiv 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 Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics 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.

Published as SciPost Phys. 10, 148 (2021)

We thank the editor for considering our paper for publication in SciPost.

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

- 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."

### Submission & Refereeing History

Resubmission 2010.00607v3 on 21 May 2021
Submission 2010.00607v2 on 5 February 2021

## Reports on this Submission

### Report

The changes are fine, and I recommend publication in SciPost.

• validity: -
• significance: -
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### Report

The authors have taken into account all the comments and suggestions in the referee report, and clarified their work accordingly. I recommend publication of this revised version in SciPost Physics.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -