Characterizing dynamical behavior in topological open systems with boundary dissipation
Phys. Rev. B 111, 214304 – Published 12 June, 2025
DOI: https://doi.org/10.1103/7997-q51d
Abstract
We investigate the dynamics of the Su-Schrieffer-Heeger model with boundary dissipation described by Lindblad master equations and unravel distinct dynamical features in the topologically different phases of the underlying Hamiltonian. By examining the long-time damping dynamics, we uncover a dynamical duality phenomenon between the weak and strong dissipation regions which exists only in the topologically nontrivial phase, linked to the structure of the Liouvillian spectra, particularly the stripe closest to the steady state. When dissipation is confined to a single boundary, the dynamical duality phenomenon still exists. Under this condition, the Liouvillian gap fulfills an exponential size scaling relation in the topologically nontrivial phase and a power-law size scaling relation in the topologically trivial phase. Within the topologically nontrivial region, we identify the existence of boundary-localized dark states in the thermodynamical limit, which are responsible for the exponential size decay of Liouvillian gap.
