Controlling Dissipative Topology Through Floquet Driving: From Transient Diagnostics to Boundary States Isolation

Abstract

Engineering dissipative dynamics in open quantum systems is under active focus, especially in topological settings where resilient edge modes are expected to exhibit decay rates distinct from the bulk. In this letter, we propose an efficient dynamical scheme to discern such long-lived excitations. Employing a Floquet-Lindblad framework, we explore how periodic driving reshapes the key features of a paradigmatic topological model, namely a Creutz ladder. Our results bear testimony to a drive-induced unipolar-bipolar transition in the Liouvillian skin effect, which gets dynamically manifested as a chiral-helical damping crossover. Such a transition effectively rescales the bulk localization length, giving rise to a polarization drift that we identify as a new invariant for efficient diagnosis of the nontrivial phases. As the transition becomes more gradual via tuning drive-rescaled parameters, we uncover signatures of a scale-free localization where skin and extended modes co-exist with distinct decay rates. The emergent hierarchy of the decay rates yields two disparate timescales: a chiral wavefront that rapidly empties the bulk followed by a long-lived regime dominated by robust edge modes. Overall, our results provide convincing evidence that periodic driving serves as a powerful handle to manipulate dissipative topological phases and dynamically isolate the boundary modes.

Figures (7)

• Figure 1: Schematic representation of a Creutz ladder (weakly) coupled to an environment, with dissipation acting solely on the $A$ sublattice edge.
• Figure 2: (a–d) Representative eigenstate profiles for selected values of $t_V$. Unipolar localization with FGBZ radius $<1$ evolves into a bipolar configuration as $t_V$ increases, followed by skin suppression associated with a reversal of eigenstate polarization. (e) Drive-renormalized localization length, $\xi_{\text{driven}}$ showing periodic modulation and divergences at the skin-suppression points. Here we have chosen $L=100, t_D=t_H=0.5,\gamma_l=\gamma_g=0.3$, and $T=2$.
• Figure 3: (a) Floquet rapidity spectrum versus $t_V$, color‐coded by the real eigenvalues of $X_F$. (b) Polarization drift $D_P$ as a function of $t_V$, showing a one-to-one correspondence with the spectral features in panel (a). Here, we have chosen $L=100$, $t_D=t_H=0.5$, $\gamma_l=\gamma_g=0.3$, and $T=2$.
• Figure 4: (a),(b) Floquet rapidity spectrum as a function of $t_V$, color–coded by the real eigenvalues of $X_F$ and the corresponding dIPR values, respectively. A direct comparison shows that left/right skin modes exhibit enhanced decay rates, whereas topological boundary modes retain the smallest decay rates. (c) Time evolution of $\Delta P(t)$, revealing two distinct dynamical regimes: an initial short–time decay governed by a rapidly damped chiral wavefront that depletes the bulk, followed by a long–time regime dominated by robust edge modes. Here, $L=100$, $t_D=1.5$, $t_H=0.5$, $\gamma_l=\gamma_g=0.3$, and $T=2$.
• Figure 5: (a) MIPR as a function of $t_D$, revealing two distinct regimes: an anti–$\mathcal{PT}$–symmetric phase for $t_D < t_{D_c}$, where all states are skin–localized with nearly identical decay rates, and an anti–$\mathcal{PT}$–broken phase for $t_D > t_{D_c}$, where a subset of states becomes delocalized and acquires decay rates distinct from the skin modes. (b) Evolution of the PBC spectrum from point-gap to line-gap topology across $t_{D_c}$, signaling the breakdown of LSE. (c) Finite–size scaling of MIPR, showing system-size–independent localization for $t_D < t_{D_c}$ and a growing localization length for $t_D > t_{D_c}$. Here, $t_D=0.5$ ($t_D < t_{D_c}$) and $t_D=1.5$ ($t_D > t_{D_c}$), $t_H=0.5$, $\gamma_l=\gamma_g=0.3$, and $T=2$.