Interacting spin chains and ladders are known to support a plethora of quantum phases with complex ground-state phase diagrams. In this work, we study a large family of such models and determine precise, explicit conditions under which an exact dimer state is guaranteed to be their ground 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 phase diagrams of a wide class of spin chains and ladders, including those with anisotropic and arbitrary-range interactions.

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• Magnetic order
• Peierls transition
• Spin-singlet pairing
• Spin-triplet pairing
• 1-dimensional spin chains
• Magnetic systems
• Quantum many-body systems
• Strongly correlated systems
• Exact diagonalization
• Exact solutions for many-body systems
• Finite-size scaling
• Heisenberg model
• Quantum spin chains
• Spin ladders
• XYZ model