Controlling the classical spin chain

The dynamics of quantum many-body systems in the presence of unitary operations, measurement, and feedback have uncovered a class of “control transitions,” that push the system towards a dark state of the unitary dynamics. These transitions have a well-defined classical limit and describe the classical control of chaos. In most cases considered so far the classical transitions investigated have been focused on the single particle limit, here we extend these ideas to a many-body classical control transition. Starting from the dynamics of the Heisenberg spin chain we construct a model that has a control transition by pushing the dynamics to a spin spiral state in the middle of the energy spectrum. We study the nature of this non-equilibrium phase transition and play close attention to the nature and distribution of the leading Lyapunov exponent across the transition.