Magnon dispersion and Single hole motion in 2D frustrated antiferromagnets with four-sublattice structures

We study a two dimensional spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet in a square lattice using the linearized spin wave theory recognizing the 4-sublattice nature of the underlying magnetic lattice. Multiple magnon modes with optical and acoustic branches about the stable Neel ordered and double acoustic branches about the columnar reference states are obtained for small and large values of $\lambda(=J_2/J_1)$ respectively. An additional uniaxial anisotropy, for large $\lambda$, can lead to distinct spin gaps in such systems, as also witnessed experimentally. The single hole spectral behavior in a 2D $t-J_1-J_2$ model, for small frustration, is then calculated within the non-crossing approximation. Our results match fairly well with exact diagonalization results from a $4\times4$ cluster. Hole spectral features and their evolution with $\lambda$ resulting in "water-fall"-like smooth spectral weight transfer are discussed. Hole energy bands are identified and the corresponding energy-shift and reduction in width with spin-frustration are indicated.