Equivalence between XY and dimerized models

The spin-1/2 chain with XY anisotropic coupling in the plane and the XX isotropic dimerized chain are shown to be equivalent in the bulk. For finite systems, we prove that the equivalence is exact in given parity sectors, after taking care of the precise boundary conditions. The proof is given constructively by finding unitary transformations that map the models onto each other. Moreover, we considerably generalized our mapping and showed that even in the case of fully site-dependent couplings the XY chain can be mapped onto an XX model. This result has potential application in the study of disordered systems.