Exact dimer ground states of long-range spin chains and ladders

Interacting spin chains and ladders are known to support a plethora of quantum phases withcomplex ground-state phase diagrams. In this work, we study a large family of such models anddetermine precise, explicit conditions under which an exact dimer state is guaranteed to be theground state. These general conditions are validated for various generalizations of the Majumdar-Ghosh model using exact diagonalization. Our results provide exact reference points in the phasediagrams of a wide class of spin chains and ladders, including those with anisotropic and arbitrary-range interactions.