Infinite temperature adiabatic flows and quantum many-body scar states in a chaotic system

Under any operation in many-body chaotic systems, quantum states usually experience dissipation. However, this dissipation can be drastically suppressed through the application of additional appropriate control fields, as is done in counterdiabatic driving. Here, we restrict control to few-body operations and draw flows of the optimal path for quantum control in a non-integrable Ising chain. We find that these flows are highly anisotropic; we can realize almost dissipationless driving in one direction while dissipation is hard to reduce in the perpendicular direction. This indicates that the choice of the path is crucial for quantum operations in many-body chaotic systems. Furthermore, states which are eigenstates of the counterdiabatic term are shown to exhibit small dissipation even without counterdiabatic fields, and are closely related to quantum many-body scar states and many-body dark states.