The Ising quantum chain with defects. Pt. 2

Haye Hinrichsen B

Uwe Grimm

Malte Henkel, A. Patkós, Martin Schlottmann

Degang Zhang, Bo‐Zang Li, Yun Li

Robert A. Henry, Murray T. Batchelor

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}_N ℤ N -symmetric clock models. In 1989 Baxter discovered a non-Hermitian but \mathcal{PT} 𝒫 𝒯 -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} 𝒫 𝒯 -symmetric at these exceptional points, their proximity can have a profound impact on the model on the \mathcal{PT} 𝒫 𝒯 -symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

Francis A. Bayocboc, Jacek Dziarmaga, Marek M. Rams +1 more

We identify persistent oscillations in a nonintegrable quantum Ising chain. In the integrable chain with nearest-neighbor interactions, the nature, origin, and decay of post-transition oscillations are tied to the Kibble-Zurek mechanism. Remarkably, when coupling to the next-nearest neighbor is added, the resulting nonintegrable ``zigzag'' chain (still in the quantum Ising universality class) supports persistent oscillation: Topological defects (kinks) appear as a result of the quantum phase transition. However, in a ``zigzag'' Ising chain defects can form Cooper pairs. The oscillation of the Cooper-pair condensate has a frequency that depends on the binding energy gap between the paired and the unpaired defects, so it can be excited by resonant driving. While one might have expected that the integrability-breaking zigzag coupling causes relaxation, the oscillations we identify are persistent: Their longevity in our simulations is likely limited only by numerical accuracy. This oscillation of the Cooper-pair condensate of kinks is a manifestation of quantum coherence and should be experimentally accessible.