Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States

Abstract

Non-equilibrium dynamics in non-Hermitian systems has attracted significant interest, particularly due to the skin effect and its associated anomalous phenomena. Previous studies have primarily focused on initial states with a definite particle number. Here, we present a systematic study of non-reciprocal quench dynamics in the pairing states with indefinite particle number. Our study uncovers a range of novel behaviors. Firstly, we demonstrate a universal tendency towards half-filling of particle density at late times. At early times for certain initial states, we observe a chiral wavefront in both particle number distribution and charge inflow, associated with a sharp decrease in particle number. Furthermore, we find that non-Hermiticity could enhance the growth of entanglement in the initial stages of evolution. In the intermediate time regime, the characteristic skin effect leads to particle accumulation on one side, leading to a pronounced reduction in entanglement entropy. Moreover, our results reveal the presence of the quantum Mpemba effect during the restoration of U(1) symmetry. Our findings open new avenues for exploring exotic dynamic phenomena in quantum many-body systems arising from the interplay of symmetry breaking and non-Hermiticity.

Figures (3)

• Figure 1: (a) Evolution of the total particle number starting from various initial tilted ferromagnetic states. (b) Dynamics of local particle density $n_{j}$. Characteristic timescales $\tau_{1}$ and $\tau_{2}$ are marked by horizontal dashed lines. Dynamics of (c) current density $I_{j}$, and (d) particle inflow rate $\sigma_{j}$. In (c), positive current indicates flow from left to right, and negative current from right to left. In (d), positive inflow represents particle gain, and negative inflow represents particle loss. For (b)-(d), the initial state is the tilted ferromagnetic state with $\theta=\pi/6$. The system size is $L=64$ and the non-reciprocity strength is $\gamma=0.8$ for all figures.
• Figure 2: Entanglement entropy under open boundary conditions. (a), (b) and (c) correspond to $\gamma =0.0$, 0.2 and 0.6, respectively, where the legends represent different tilted angles. The traced subsystem $B$ with length $l=6$ is located at the left end of the system. The total system size is $L=64$ and the characteristic timescale $\tau_{1}$ is marked by vertical dashed line.
• Figure 3: Entanglement asymmetry under the open boundary conditions. (a), (b) and (c) correspond to $\gamma=0.0$, $0.2$ and $0.6$, respectively, where the legends represent different tilted angles. The traced subsystem $B$ with length $l=12$ is located at the left end of the system. The total system size is $L=64$.