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Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
by Yin Tang, Qianyu Liu, Qicheng Tang, Wei Zhu
Submission summary
| Authors (as registered SciPost users): | Yin Tang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202412_00032v2 (pdf) |
| Date accepted: | Dec. 4, 2025 |
| Date submitted: | Nov. 11, 2025, 2:17 a.m. |
| Submitted by: | Yin Tang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Conformal fields with boundaries give rise to rich critical phenomena that can reveal information about the underlying conformality. While the existing studies focus on Hermitian systems, here we explore boundary critical phenomena in a non-Hermitian quantum 5-state Potts model which exhibits complex conformality in the bulk. We identify free, fixed and mixed conformal boundary conditions and observe the conformal tower structure of energy spectra, supporting the emergence of conformal boundary criticality. We also studied the duality relation between different conformal boundary conditions under the Kramers-Wannier transformation. These findings should facilitate a comprehensive understanding for complex CFTs and stimulate further exploration on the boundary critical phenomena within non-Hermitian strongly-correlated systems.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
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As suggested by the first two referees, we have improved the overall readability of the manuscript by revising the English presentation throughout.
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As suggested by the second referee, we have clarified the implementation of the boundary fields by specifying that $g_L = g_R = 20$ and added related discussion on boundary RG flows in the Discussion section.
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As suggested by the second referee, we have clarified in Tables 2 and 3 how the normalization of the spectra is performed and explained why certain scaling dimensions are exact by construction.
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Following the second referee’s comment, we have added the extracted complex spin-wave velocity ($v = 2.7205 - 0.6906i$) in the caption of Fig. 2 for reference.
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As suggested by the third referee, we have clarified that the construction of Cardy and Ishibashi states applies only to rational BCFTs.
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As suggested by the third referee, we have revised the introduction to clarify that while generic irrational BCFTs are difficult to treat, cases with enlarged algebras (such as those in Potts and $O(n)$ loop models) admit exact algebraic treatments even for non-unitary irrational theories.
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As suggested by the third referee, we have corrected minor inaccuracies in Section~2.
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As suggested by the third referee, we have added a short review at the end of Section~2 summarizing the main results of algebraic construction of irrational Potts BCFTs with real $Q<4$, where the boundary Temperley--Lieb algebra allows one to build annulus partition functions analytically continued in $Q$.
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As suggested by the third referee, we have added proper references and contextual explanations when introducing the “blob boundary conditions.”
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Following the third referee’s suggestion, we now explicitly state the system size used in our exact diagonalization ($L = 6$–$11$), and have clarified the representation-theoretical identification in Fig.~3. The “lowest $S_5$ vector operator” is now described as the most relevant operator in the 4-dimensional standard representation.
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As suggested by the third referee, we have added a paragraph in Sec.~4.2.1 explaining that the coefficients in Eq.~(50) could be derived from the two-boundary Temperley–Lieb annulus partition function with parameters $r_1=r_2=r_{12}=1$, and that they correspond to even-order Chebyshev polynomials of the second kind.
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We have added a new discussion at the end of Sec.~4.2.2 showing how the results for fixed boundary conditions can be derived from the analytic 2BTL framework.
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We have reanalyzed the numerical data and completely rewritten Sec.~4.2.3 to clarify the free/fixed–mixed boundary results, connecting them more explicitly with the analytic 2BTL predictions.
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As suggested by the third referee, we have corrected the terminology in Sec.~4.3, now referring to the “wired” boundary condition instead of the “fixed boundaries,” inserted the missing global factor of $Q$ in Eq.~(54), and revised the discussion of the duality.
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Finally, we have rewritten the concluding Section~5 to provide a more balanced summary of our contributions.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report #1 by Jesper Lykke Jacobsen (Referee 3) on 2025-11-11 (Invited Report)
Strengths
2-The discussion how many of these results emerge from the analytic continuation of results on boundary loop models has been much improved with respect to the previous version.
Weaknesses
Report
Requested changes
1-Given the very extensive changes and improvements that follow directly from the remarks made in my report on the first version of this manuscript (several pages of text have been added), I think it would be appropriate that the authors recognize this in the acknowledgments.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)