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Elaborating the phase diagram of spin1 anyonic chains
by Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur
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Submission summary
Authors (as registered SciPost users):  Jesper Lykke Jacobsen · Hubert Saleur · Eric Vernier 
Submission information  

Preprint Link:  https://arxiv.org/abs/1611.02236v2 (pdf) 
Date accepted:  20170214 
Date submitted:  20170209 01:00 
Submitted by:  Vernier, Eric 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We revisit the phase diagram of spin1 $su(2)_k$ 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 spin1 anyonic chains.
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, sidebyside 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 finitesize data with some finitesize extrapolation. However, in the current form this finitesize 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 finitesize 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 nonzero. This is in agreement with the fact that magnetic excitations (corresponding to holes in the Fermi sea) of the sixvertex model in its massive phase have a nonzero 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
Published as SciPost Phys. 2, 004 (2017)