Shortcuts to adiabaticity in open quantum critical systems

Abstract: We study shortcuts to adiabaticity (STAs) through counterdiabatic driving in quantum critical systems in the presence of dissipation. We evaluate unitary as well as nonunitary controls, such that the system density matrix follows a prescribed trajectory corresponding to the eigenstates of a time-dependent reference Hamiltonian at any instant of time. The strength of the dissipator control term for the low-energy states shows universal scaling close to criticality. Using the example of free-fermionic systems, in particular, the transverse-field Ising model, we show that in contrast to STAs in closed quantum critical systems, here, STAs may require multibody interactions terms, even away from criticality, owing to the change in entropy of the time-dependent target state. Further, the associated heat current shows an extremum, while power dissipation changes curvature, close to criticality, and analogous to unitary control, no operational cost is associated with implementation of the exact counterdiabatic Hamiltonian. We believe the counterdiabatic protocol studied here could be of fundamental importance for understanding STAs in many-body open quantum systems and could be highly relevant for varied topics involving open many-body quantum systems, such as quantum computation and many-body quantum heat engines.