Title: Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss,
Abstract: We investigate the Anderson localization in non-Hermitian
Aubry-André-Harper (AAH) models with imaginary potentials added to lattice
sites to represent the physical gain and loss during the interacting processes
between the system and environment. By checking the mean inverse participation
ratio (MIPR) of the system, we find that different configurations of physical
gain and loss have very different impacts on the localization phase transition
in the system. In the case with balanced physical gain and loss added in an
alternate way to the lattice sites, the critical region (in the case with
p-wave superconducting pairing) and the critical value (both in the situations
with and without p-wave pairing) for the Anderson localization phase transition
will be significantly reduced, which implies an enhancement of the localization
process. However, if the system is divided into two parts with one of them
coupled to physical gain and the other coupled to the corresponding physical
loss, the transition process will be impacted only in a very mild way. Besides,
we also discuss the situations with imbalanced physical gain and loss and find
that the existence of random imaginary potentials in the system will also
affect the localization process while constant imaginary potentials will not.