Nonadiabatic dynamics of a dissipative spin chain in a transverse magnetic field

We consider a non-Hermitian Hamiltonian in order to effectively describe a dissipative spin chain in a transverse magnetic field. The model Hamiltonian is technically transformed to mimic the famous well known Landau-Zener two-level model. The time evolution of the transition probabilities is formulated and derived in terms of the normalized density operator of the model. The dynamics of this quantum open system is solved analytically in a number of relevant cases and influences of physical parameters are revealed and analyzed. In particular, the density of kinks, magnetization and coherence are defined and calculated analytically. These parameters as well as the transition probabilities are found to depends on the symmetric part of the anisotropic terms of the system's Hamiltonian. These analytical results are in good accordance with the nonadiabatic change observed experimentally in some antiferromagnetic 1/2-spin systems such as TiOCl, LiCuVO4, CuGeO3 and NaV2O5. Moreover, the time-dependent kink density expression follows the Kibble-Zurek mechanism irrespective of the other parameters of the quantum open system.