## SciPost Submission Page

# Elaborating the phase diagram of spin-1 anyonic chains

### by Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur

#### - Published as SciPost Phys. 2, 004 (2017)

### Submission summary

As Contributors: | Jesper Lykke Jacobsen · Hubert Saleur · Eric Vernier |

Arxiv Link: | https://arxiv.org/abs/1611.02236v2 |

Date accepted: | 2017-02-14 |

Date submitted: | 2017-02-09 |

Submitted by: | Vernier, Eric |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### Abstract

We revisit the phase diagram of spin-1 $su(2)_k$ anyonic chains, originally studied by Gils {\it et. al.} [Phys. Rev. B, {\bf 87} (23) (2013)]. These chains possess several integrable points, which were overlooked (or only briefly considered) so far. Exploiting integrability through a combination of algebraic techniques and exact Bethe ansatz results, we establish in particular the presence of new first order phase transitions, a new critical point described by a $Z_k$ parafermionic CFT, and of even more phases than originally conjectured. Our results leave room for yet more progress in the understanding of spin-1 anyonic chains.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 2, 004 (2017)

### Author comments upon resubmission

In the present version (v2), corrections were made in order to take in account of all received remarks.

In particular, the following changes were made :

### List of changes

- Regarding the remark of Report 53 that

{\it

It would be instructive to contrast the earlier phase diagrams, now shown in Fig. 1, with the results of the current study, shown in Fig. 8, side-by-side at the beginning of the paper, e.g. in a new figure 1.}

We agree with this comment, however space and readability constraints made very inconvenient to put figures 1 and 8 side by side. We have instead moved fig. 8 to the beginning of the paper, where it can more easily be compared with fig. 1.

- Regarding the remark of Report 53 that

{\it

Figure 2 shows some numerical finite-size data with some finite-size extrapolation. However, in the current form this finite-size extrapolation appears to be dominated by the *smallest* system sizes with a rather noticeable discrepancy for the largest system sizes. There is no need to fit *all* the finite-size data, in fact it would be much more appropriate to only fit the largest system sizes for the “2j=2” data sets. The extrapolated gap would be noticeably smaller. Is this still sufficient numerical evidence for a gapped phase? }

We have replaced the extrapolations on figure 3 (prevously fig. 2) by linear fits excluding the smallest system sizes. The extrapolated gap is indeed smaller, but still manifestly non-zero. This is in agreement with the fact that magnetic excitations (corresponding to holes in the Fermi sea) of the six-vertex model in its massive phase have a non-zero gap.

- Regarding the remark of Report 53 that

{\it In Figure 6 it would be informative to also label the indicated field by their topological sector.}

We have added on the legend of Figure 7 (previously fig. 6) information about the topological charge of all indicated levels

- In figure 4 (formerly figure 3), we have changed the green color to orange, in order to improve its readability.

- Regarding remarks of Reports 32 and 37, we have specified the range of values of $k$ for which our results hold. More precisely, most of our conclusions are formulated for generic $k\geq 4$, but when necessary we have treated separately the cases $k>4$ and $k=4$.

In addition, we have refered to the suggested litterature for the $k=4$ case, for which we thank the author of Report 37.

- We have also improved the introduction in order to meet the suggestions of Report 53