Hamiltonian non-Hermicity: Accurate dynamics with the multiple Davydov D2Ansätze.

We examine the applicability of the numerically accurate method of time dependent variation with multiple Davydov Ansätze (mDA) to non-Hermitian systems. As illustrative examples, three systems of interest have been studied, a non-Hermitian system of dissipative Landau-Zener transitions, a non-Hermitian multimode Jaynes-Cummings model, and a dissipative Holstein-Tavis-Cummings model, all of which are shown to be effectively described by the mDA method. Our findings highlight the versatility of the mDA as a powerful numerical tool for investigating complex many-body non-Hermitian systems, which can be extended to explore diverse phenomena such as skin effects, excited-state dynamics, and spectral topology in the non-Hermitian field.