Confluences of exceptional points and a systematic classification of quantum catastrophes

Znojil, Miloslav

doi:10.1038/s41598-022-07345-7

Cited by 4 publications

(3 citation statements)

References 81 publications

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“…Thus each quasienergy degeneracy is in fact a set of N L − N L−1 2-fold degeneracies, or 1 2 (N L − N L−1 ) coincident two-level EPs. Such coincident EPs have recently appeared in the literature and are termed confluent EPs [26,27]. In particular, the passage of a system through such an EP has interesting physical properties.…”

Section: Discussionmentioning

confidence: 99%

Exceptional points in the Baxter-Fendley free parafermion model

Henry

Batchelor

2023

SciPost Phys.

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Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to \mathbb{Z}_NℤN-symmetric clock models. In 1989 Baxter discovered a non-Hermitian but \mathcal{PT}𝒫𝒯-symmetric model directly generalising the Ising chain, which was later described by Fendley as a free parafermion spectrum. By extending the model’s magnetic field parameter to the complex plane, it is shown that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general \mathcal{PT}𝒫𝒯-symmetric at these exceptional points, their proximity can have a profound impact on the model on the \mathcal{PT}𝒫𝒯-symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

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Section: Discussionmentioning

confidence: 99%

Exceptional points in the Baxter-Fendley free parafermion model

Henry

Batchelor

2023

SciPost Phys.

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“…Such a coincidence of a macroscopic number of EPs is an unusual phenomenon. The recent work of Znojil [23,24] suggests that such coincident EPs, referred to as confluent, have special physical properties.…”

Section: Hamiltonian Exceptional Pointsmentioning

confidence: 99%

Exceptional Points in the Baxter-Fendley Free Parafermion Model

Henry¹,

Batchelor²

2023

Preprint

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Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a simple generalisation of this idea to Z N -symmetric models. In 1989 Baxter discovered a non-Hermitian but PT -symmetric model directly generalising the Ising chain which was much later recognised by Fendley to be a free parafermion spectrum. By extending the model's magnetic field parameter to the complex plane, we show that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general PT -symmetric at these exceptional points, their proximity can have a profound impact on the model on the PT -symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field). Contents 5 Other Degeneracies of H 11 6 Exceptional Points and Positive Real λ 11 7 Conclusion 12

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“…The emergence of geometric Berry phases is quite common in non-Hermitian systems, but the acquired phases can be largely enhanced by encircling DPs or EPs [37][38][39] . Moreover, DPs and EPs are useful in testing and classifying phases and phase transitions 40,41 . For example, a Liouvillian spectral collapse in the standard Scully-Lamb laser model occurs at a quantum DP 42,43 .…”

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Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

et al. 2023

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Nontrivial spectral properties of non-Hermitian systems can lead to intriguing effects with no counterparts in Hermitian systems. For instance, in a two-mode photonic system, by dynamically winding around an exceptional point (EP) a controlled asymmetric-symmetric mode switching can be realized. That is, the system can either end up in one of its eigenstates, regardless of the initial eigenmode, or it can switch between the two states on demand, by simply controlling the winding direction. However, for multimode systems with higher-order EPs or multiple low-order EPs, the situation can be more involved, and the ability to control asymmetric-symmetric mode switching can be impeded, due to the breakdown of adiabaticity. Here we demonstrate that this difficulty can be overcome by winding around exceptional curves by additionally crossing diabolic points. We consider a four-mode $${{{{{{{\mathcal{PT}}}}}}}}$$ PT -symmetric bosonic system as a platform for experimental realization of such a multimode switch. Our work provides alternative routes for light manipulations in non-Hermitian photonic setups.

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Confluences of exceptional points and a systematic classification of quantum catastrophes

Cited by 4 publications

References 81 publications

Exceptional points in the Baxter-Fendley free parafermion model

Exceptional points in the Baxter-Fendley free parafermion model

Exceptional Points in the Baxter-Fendley Free Parafermion Model

Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

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