Exact staggered dimer ground state and its stability in a two-dimensional magnet

Finding an exact solution for interacting quantum many-body systems is a non-trivial task. There are only a few problems where we know the exact solution, often in a narrow parameter space. We propose a spin-1/2 Heisenberg model with a unique and exact dimer ground state at J_2/J_1=1/2. A dimer state is a product of spin-singlets on dimers (some distinct bonds). We investigate the model employing bond-operator mean-field theory and exact numerical diagonalization. These tools correctly verify the exactness of the dimer ground state at the exact point (J_2/J_1=1/2). As we move away from the exact point, the dimer order melts and vanishes, where the spin-gap becomes zero. The mean-field theory with harmonic approximation indicates that the dimer order remains for -0.35≲ J_2/J_1≲ 1.35. In non-harmonic approximation, the upper critical point lowers by 0.28 to 1.07, whereas the lower critical point remains intact. The model gives Néel order as we move below the lower critical point and stripe magnetic order above the upper critical point.