SciPost Submission Page
Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
by Sk Asrap Murshed and Bitan Roy
Submission summary
| Authors (as registered SciPost users): | Bitan Roy |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00005v2 (pdf) |
| Date submitted: | 2024-11-20 04:02 |
| Submitted by: | Roy, Bitan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The energy spectra of linearly dispersing gapless spin-3/2 Dirac fermions display birefringence, featuring two effective Fermi velocities, thus breaking the space-time Lorentz symmetry. Here, we consider a non-Hermitian (NH) generalization of this scenario by introducing a masslike anti-Hermitian birefringent Dirac operator to its Hermitian counterpart. The resulting NH operator shows real eigenvalue spectra over an extended NH parameter regime, and a combination of non-spatial and discrete rotational symmetries protects the gapless nature of such quasiparticles. However, at the brink of dynamic mass generation, triggered by Hubbardlike local interactions, the birefringent parameter always vanishes under coarse grain due to the Yukawa-type interactions with scalar bosonic order-parameter fluctuations. The resulting quantum critical state is, therefore, described by two decoupled copies of spin-1/2 Dirac fermions with a unique terminal Fermi velocity, which is equal to the bosonic order-parameter velocity, thereby fostering an emergent space-time Lorentz symmetry. Furthermore, depending on the internal algebra between the anti-Hermitian birefringent Dirac operator and the candidate mass order, the system achieves the emergent Yukawa-Lorentz symmetry either by maintaining its non-Hermiticity or by recovering a full Hermiticity. We discuss the resulting quantum critical phenomena and possible microscopic realizations of the proposed scenarios.
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
Report #2 by Carlo Beenakker (Referee 1) on 2025-1-6 (Invited Report)
Strengths
- remarkable finding of an emergent relativistic symmetry in an open quantum system
- timely contribution to the active field of non-Hermitian quantum mechanics
Weaknesses
- no immediate physical realisation available
Report
I was asked to report on this manuscript after two referees gave conflicting recommendations. The critical referee objected that the Hamiltonian, while being non-Hermitian, still had a real spectrum, which would obscure the impact of the non-Hermiticity. In the literature this class of Hamiltonians is actually of particular interest, since it allows to distinguish effects from the non-orthogonality of the eigenstates from more mundane effects of complex eigenvalues. I do agree with the critical referee that the application of the model studied here to an experimentally accessible system is uncertain, but I would not find this an objection that should stand in the way of publication: The paper studies a highly non-trivial problem of strongly interacting fermions in a system coupled to an environment, with implications for our fundamental physical understanding of the emergence of relativistic symmetries. I would consider a study of this type suitable for publication in SciPost Physics.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report
The referees have significantly revised the manuscript and in doing so have addressed my concerns. I can recommend the paper for publication. (Please correct the typo "cpupling" in the caption of Fig. 4)
Recommendation
Publish (meets expectations and criteria for this Journal)