Sweeping through the critical region

Sara Zamani, J. Naji, Rouhollah Jafari +1 more

The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of linear time dependent magnetic field, is investigated using the notion of dynamical quantum phase transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose of this work is to search fundamental concepts such as scaling and universality at the ramped quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs, can be moved by tuning the driven frequency and consequently the presence of or absence of DQPTs can be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a ramp across the single quantum critical point, the critical mode at which DQPTs occur is classified into three regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the square root of the sweep velocity, the pre-saturated (PS) region, and the saturated (S) region where the critical mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points, the critical modes disclose just the KZ and PS regions. On the basis of numerical simulations, we find that the dynamical free energy scales linearly with time, as approaches to DQPT time, with the exponentν=1±0.01for all sweep velocities and driven frequencies.

Javier Brey, Robert B. Jones

F.J.W. Hahne

Rong 蓉 Chang 常, Sheng-Chang Li

Abstract The control of adiabatic dynamics is essential for quantum manipulation. We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau–Zener model with periodic modulation. We obtain adiabatic phase diagrams in the (ω, δ) parameter space, where the adiabatic region is bounded by the modulating frequency ω greater than a critical value ω c and the non-reciprocal parameter δ less than one. The results show that the adiabaticity of the system is not sensitive to the modulating amplitude. We find that the critical modulating frequency can be expressed as a power function of the modulating period number or the sweeping rate. Our findings suggest that one can change the adiabatic region or improve the adiabaticity by adjusting the parameters of both the modulating and the sweeping fields, which provides an effective means to flexibly control the adiabatic dynamics of non-reciprocal systems.

Andrea Fubini, G. Falci, Andreas Osterloh

We analyse the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field is tuned through the critical point with a linear ramping. The excitation probability is obtained exactly and is compared to previous studies and to the Landau–Zener formula, a long time solution for non-adiabatic transitions in two-level systems. The exact time dependence of the excitations density in the system allows us to identify the adiabatic and diabatic regions during the sweep and to study the mesoscopic fluctuations of the excitations. The effect of white-noise is investigated, where the critical point transmutes into a non-Hermitian 'degenerate region'. Besides an overall increase of the excitations during and at the end of the sweep, the most destructive effect of the noise is the decay of the state purity that is enhanced by the passage through the degenerate region.