Wave-packet and entanglement dynamics in a non-Hermitian quantum system

Synopsis

Quantum mechanics described by a non-Hermitian Hamiltonian has been of much interest recently. In reality, such a Hamiltonain is associated with an open quantum system. Here, we will particularly focus on a specific type of non-Hermiticity, represented by a non-reciprocal (asymmetric) hopping in a 1D tight-binding model: the so-called Hatano-Nelson model [1]. Effects of on-site disorder and inter-particle interaction is also taken into account. In the regime of weak disorder, the eigen wave functions are extended, and corresponding eigen energies are complex under the periodic boundary. In the time evolution an initial wave packet with many eigenstates superposed tends to evolve into a single eigen state with a maximal imaginary part. This results in a non-monotonic time evolution of the entanglement entropy in the regime of intermediate disorder; in the regime, collapse of the superposition is not too fast but occurs in the time scale comparable to the growth of the entanglement entropy [2,3]. The effect of on-site disorder W is also non-monotonic. With increasing W, it first enhances the entanglement entropy then suppresses it. After a long enough time in the quench dynamics, the entanglement entropy in the clean and non-interacting limit obeys a logarithmic scaling, reminiscent of the one known (in the Hermitian case) in conformal field theory.

[1] N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996).

[2] T. Orito and K.-I. Imura, Phys. Rev. B 105, 024303 (2022).

[3] T. Orito and K.-I. Imura, in preparation.