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Magnetic excitations of diagonally coupled checkerboards

By using quantum Monte Carlo based stochastic analytic continuation (QMC-SAC) and spin wave theory, we study magnetic excitations of Heisenberg models with diagonally coupled checkerboard structures. We consider three kinds of checkerboard models (DC 2 × 2, DC 3 × 3, and CDC 3 × 3) consisting nearest-neighbor strong J 1 and weak J 2 antiferromagnetic interactions. When the coupling ratio g = J 2/J 1 approaches 1, all three diagonal checkerboards have the same long-range antiferromagnetic Néel order at T = 0. When g decreases, the quantum fluctuation can drive DC 2 × 2 model to quantum paramagnetic state, while DC 3 × 3 and CDC 3 × 3 models still have the long-range Néel order. By calculating the magnetic excitations at different coupling ratios, we find that the low-energy part of magnetic excitations calculated by QMC-SAC can be well explained by the spin wave theory. However, the high-energy parts even deep in the long-range antiferromagnetic phase are beyond the spin wave description. Compared to the g = 1 uniform square lattice, the high-energy excitations are more rich in our models. Our study may also draw the attention to the high-energy exctitaions beyond the spin wave theory.