Anomalous thermalization by dissipation in quantum XY model

We consider the dynamics in the quantum XY model with boundary dissipation. This model after fermionization gives the topological $p$-wave superconducting model with two localized edge modes at the two ends separated from the bulk spectra by a finite energy gap. The dissipation can induce coupling between the ground states manifold and all the excited bands, which induces thermalization in a characteristic time $T^*$. In the long time limit, the density matrix will approaches the maximal mixed state in each even and odd parity subspaces, with thermalization determined by the single particle dynamics. We find that the thermalization time $T^* \propto N^3/\gamma $ in the weak dissipation limit, where $N$ is the chain length and $\gamma$ is the dissipation rate; while in the strong dissipation limit, $T^* \propto \gamma N^3$. These analytical results are counterintuitive because it means weak dissipation can induce strong thermalization, while strong dissipation can induce weak thermalization. We find that these two limits correspond to two different physics, which are explained by mapping the single fermion dynamics to a non-Hermitian model. Even in the long chain limit, the dissipation will exhibit strong odd-even effect from the oscillation of wave function at the two ends. These results shade new insight into the dynamics of topological qubits and their stabilities in environment.