Exact solution of anisotropic antiferromagnetic alternating Heisenberg–Ising spin chain

We extend the spin (=12) chain model with alternating Heisenberg and Ising couplings to the case of anisotropic Heisenberg exchange. The model can be mapped to a bilinear fermion model, which is exactly solved via Jordan–Wigner and Bogoliubov transformations. We find low-energy excitations with a gap when the Ising coupling strength is not equal to 2. And this conclusion will not be changed for any kind of anisotropic Heisenberg exchange.