Fig. 4: Time evolution and decay into the DDS.
a Evolution of the purity γ(t), for different sizes. Starting from a pure CDW state, the system becomes highly mixed before starting leaking into the DDS. The dotted line shows the minimum purity possible in the DDS, corresponding to a fully mixed state. Inset: Evolution of a local observable (density). We observe that the local density relaxes to it value in the DDS in a shorter timescale compared with the time required for the system to enter the DDS. This happens independently of the system size. b Approach of the DDS, spanned by the Laughlin-like states on the narrow torus, for different system lengths L. c Purity in the DDS as a function of β. The purity of the DDS depends strongly on β, indicating that the purity can be maintained if the final state is close to the initial one. The dotted lines for the L = 15 case for the purity and density evolution are obtained from an approximation for the Lindbladian on a smaller subspace. In the approximation we neglect the terms of the evolved state ρ(t) which are smaller than a threshold ϵ = 10−5 and construct the effective Lindbladian for the remaining subspace, which has a smaller dimension. The dotted lines for L = 15 for the DDDS are obtained from the knowledge of the ADR, and simply performing a continuation of the dynamics.
