SciPost Submission Page
Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities
by Xin-Chi Zhou, Ke Wang
Submission summary
| Authors (as registered SciPost users): | Xin-Chi Zhou |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00008v1 (pdf) |
| Date submitted: | 2024-05-06 06:01 |
| Submitted by: | Zhou, Xin-Chi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The critical point of a topological phase transition is described by a conformal field theory (CFT), where the finite-size corrections to the ground state energy are uniquely related to its central charge. We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry ($\mathcal{PT}$) symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)\sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point, indicative of a non-unitary CFT. Furthermore, we discover a universal scaling function capturing the flow of a system from Dirac CFT with $c=1$ to a non-unitary CFT with $c=-2$. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points. Notably, within the realm of topological criticality, the scaling function exhibits an universal rise-dip-rise pattern, manifesting a characteristic singularity inherent in the non-Hermitian topological critical points. The analytic expression of the scaling function has been derived and is in good agreement with the numerical results.
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
Current status:
Reports on this Submission
Strengths
Not sure.
Weaknesses
Seems to re-invent well known facts, peppering them with a bit of new language, and betrays embarrassing ignorance of the literature on the side of the authors.
Report
This paper is almost exclusively formulated in the language of topological phase transitions, but from a technical point of view, it simply revisits well known facts about spin chains, non-unitarity and quantum criticality. The total lack of reference to the relevant literature in this area is embarrassing to say the least, and prevents one from appreciating what might be new in the paper, if anything. I think a complete rewriting is necessary before publication can be considered. It may then appear that the authors have discovered something interesting, but as of now, I cannot judge.
Requested changes
The free fermion model considered by the authors becomes an XX chain with boundary terms after a Jordan-Wigner transformation. The correspondence should be discussed, and the results compared with what is known in this field - see e.g. the paper by Hinrichsen Rittenberg Physics Letters B 275 (1992) 350-354 and the many references therein. See papers by Pasquier Saleur about quantum groups, see papers by Nichols Rittenberg and others about Temperley and two-boundary Temperley-Lieb algebras.
The emergence of c=-2 with open BC and c=1 with periodic BC is well known in the context of fermionic CFTs. See papers by Kausch, the whole literature about dimers, papers by Ruelle and coworkers about sand piles etc. The author's discussion of this point in the paper is particularly naive. The behavior of levels of Hamiltonians for non-unitary CFTs is studied in an old paper by Itzykson Saleur and Zuber. The behavior of entanglement in non-unitary systems is studied in a paper by Couvreur Jacobsen Saleur, and discussed in great detail in papers by Castro-Alvaredo, Doyon and Ravanini.
The study of scaling functions of central charge or effective central charge in non-unitary CFTs is familiar, and so is the zig zag behavior observed by the authors. See papers by A. Zamolodchikov, on his own or with Fendley Saleur.
I think the authors should do the job of situating their paper in the vast literature on the subject, and explain clearly what it is they think they have discovered that is new and interesting.
Recommendation
Ask for major revision