The Kibble-Zurek mechanism at exceptional points

Abstract

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.

Fig. 1

The numerically determined defect density. We plot the defect density from the normalized (blue circles) and unnormalized wavefunction (red squares) for the PT-symmetric ramp, as well as for the full non-hermitian drives (green triangles), measured from its adiabatic value. The black dashed lines denote the τ^−1/3, τ^−2/3, and τ⁻¹ scaling. The cutoff |p| < W = 10Δ₀ and 10Γ₀, respectively, does not alter the dynamics, with other values yielding similar scaling

Fig. 2

Momentum resolved defect density for the PT-symmetric ramp. The scaling and data collapse of the numerically determined momentum resolved defect density, f_PT(x) in the near-adiabatic limit is shown for several values of τ for the PT-symmetric ramp

Fig. 3

Momentum resolved defect density for the non-hermitian drive. The scaling of the numerically determined momentum resolved defect density, f_nh(x) in the near-adiabatic limit is shown for several values of τ for the full non-hermitian drive around the equilibrium EP