Interplay between Landau-Zener transition dynamic and quantum phase transition in dissipative spin chain with Dzyaloshinsky-Moriya interaction

The paper investigates the transition dynamic of a two-level system coupled uniformly to a general XY dissipative spin-chain environment with the Dzyaloshinsky-Moriya interaction. The collective effect of the spin-chain environment is studied and we obtained the exact expression of the final occupation of the system. It is observed that the increase of the decay parameter favors a shortcut to adiabaticity. In the absence of decay, the transition probability oscillations are modulated in time by the renormalized Landau-Zener (LZ) parameter that we derived. We found that in the vicinity of the critical point of the environment, depending on the strength of the system-environment coupling, the decay of the population transfer can be tailored by tuning the other parameters of the model. The critical point and thus the occurrence of the phase transition are observed to be independent of these parameters. It is shown that this quantum state transition is related to the occurrence of the quantum phase transitions in the chain. The adiabatic change for the magnetization observed in some magnetic molecules may be due to the number of spin involved in the chain, the anisotropy parameter of the chain or the external magnetic field strength.