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

by Iman Mahyaeh, Jurriaan Wouters, Dirk Schuricht

Submission summary

As Contributors: Dirk Schuricht · Jurriaan Wouters
Arxiv Link: (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
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


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:
-added Reference 24
-rewording of and around (2), (3) and (4) to clarify the algebra
-added a remark after (6)
-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)
-added Figure 5(b), adapted the caption and added a discussion after (39)
-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

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


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: -

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