# Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

### Submission summary

 As Contributors: Dirk Schuricht · Jurriaan Wouters Arxiv Link: https://arxiv.org/abs/2003.07812v3 (pdf) Date accepted: 2020-10-29 Date submitted: 2020-09-18 10:41 Submitted by: Schuricht, Dirk Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approaches: Theoretical, Computational

### Abstract

We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

Published as SciPost Phys. Core 3, 011 (2020)

### List of changes

Summary of changes in reply to both referees:
-rewording of and around (2), (3) and (4) to clarify the algebra
-corrected Eq. (8) as noted by the referee
-added a remark after (14) on the relation to spinful fermions in the case p=4 as well as Reference 33
-clarified the relation between (1) and (15) in a new paragraph after (15)
-added point R_2’ in FIg. 1
-specified the basis used to define (19) and (20)
-added discussion on the appearance of oscillations in Figure 3, in (33) and as well as after (34)
-changed notation in (42) and Fig. 11 for consistency
-mention the study of the phase transitions as open point in Section 5.5.1 and the outlook
-corrected caption of Figure 13
-extended the discussion in the last paragraph of the outlook and added references [50,51]
-updated the acknowledgement
-corrected a few typos

### Submission & Refereeing History

Resubmission 2003.07812v3 on 18 September 2020
Submission 2003.07812v1 on 18 March 2020

## Reports on this Submission

### Anonymous Report 1 on 2020-10-27 Invited Report

• Cite as: Anonymous, Report on arXiv:2003.07812v3, delivered 2020-10-27, doi: 10.21468/SciPost.Report.2120

### Report

It is regrettable that the authors did not include a discussion of the complex phases in their numerical analysis. Technically, this seems like a very simple extension, which would have made the paper more complete. But I respect the authors' choice not to do it and to publish this separately.

In my opinion, this paper can be accepted for publication.

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