Exceptional Points in the Baxter-Fendley Free Parafermion Model

Abstract

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 clock 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, 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 $PT$-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 of the model an exceptional point may appear on the real line (with negative field).

17 pages, 6 figures, Figure 3 has been changed to use the convention that the quasienergies have arguments in the range (-pi/N, pi/N], + minor changes

References in corpus (8)

• Higher-order non-Hermitian skin effect
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
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• Emergence and localization of exceptional points in an exactly solvable toy model
• Parafermionic representation of Potts-based cluster chain
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model
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