The Kibble-Zurek mechanism at exceptional points

• Published in: Nature communications Vol. 10; no. 1; pp. 2254 - 6
• Main Authors: Dóra, Balázs, Heyl, Markus, Moessner, Roderich
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 21.05.2019; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/2795; 639/766/530; Adiabatic; Critical point; Defects; Eigenvectors; Humanities and Social Sciences; Mapping; multidisciplinary; Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-019-10048-9

Exceptional points (EPs) are ubiquitous in non-Hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-Hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as τ −( d + z ) ν /( zν + 1) in terms of the usual critical exponents and 1/ τ the speed of the drive. Defect production is suppressed compared to the conventional Hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement. Universal non-equilibrium behaviour can emerge in physical systems when they are driven through a parameter regime where their energy gap closes. Dóra et al. show that the Kibble-Zurek scaling associated with exceptional points in non-Hermitian systems is distinct from the conventional Hermitian result.