Integrable systems of heterogeneous qubits

We explore an unusual type of quantum spin matter that can be realized by qubits having different physical origin, such as in bound states near defects in Dirac materials. Interactions of different qubits in this matter are described by essentially different coupling operators that do not commute with each other. We show that at least the simplest such models satisfy integrability conditions that we use to describe pseudospin dynamics in a linearly time-dependent magnetic field. Generalizing to arbitrary numbers of qubits, we construct a spin Hamiltonian, which we call the gamma-magnet. For arbitrarily strong interactions, nonadiabatic dynamics, and any initial eigenstate, we find that quantum interference suppresses spin-flips, so that the system remains close to the initial state. This effect may not have a counterpart in classical physics and can be a signature of a new type of spin ordering, which is different from both disordered spin glasses and ordered phases of spin lattices.