We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as t1/2 and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse field is changed in discrete time steps, τ, there can be excitation modes, for which coherence is maintained, provided their energy satisfies ϵkτ≈nπ with a positive integer n. If the dispersion of ϵk is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a t3/4 time dependence.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics