Shortcuts to adiabaticity in open quantum critical systems

TL;DR

This paper investigates shortcuts to adiabaticity in open quantum critical systems, analyzing how dissipation and control methods affect system dynamics, especially near critical points, with implications for quantum computation and heat engines.

Contribution

It introduces a framework for implementing counterdiabatic driving in open quantum critical systems, highlighting the need for multibody interactions and analyzing energetic costs.

Findings

Universal scaling of dissipator control near criticality

Multibody interactions are often necessary for STAs in open systems

Heat current exhibits an extremum near critical points

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.