Spin excitation spectra of the two-dimensional S =1/2 Heisenberg model with a checkerboard structure

We study the spin excitation spectra of the two-dimensional spin-1/2 Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions J₁ and J₂, and the tuning parameter g is defined as J₂/J₁ . The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When g is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the 3 ×3 checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when g is small. The gapless branch in this case can be regarded as a spin wave in Néel order formed by a "block spin" in each 3 ×3 plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.