Incommensurate Spin–Peierls Phases in the One–Dimensional Quantum Isotropic XY Model

An interest in the theoretical study of quantum spin chains exhibiting spin–Peierls phases has incredibly grown since the discovery of the first inorganic spin–Peierls compound CuGeO3 (for a review see). Although the quantum Heisenberg model is usually used as an appropriate model to describe the spin–Peierls phase transition in the available materials some generic features can be clarified within the framework of the simpler spin2 isotropic XY chain (see and references therein). The latter spin model can be reformulated using the Jordan–Wigner transformation as a one–dimensional model of tight–binding spinless fermions. As a result, the exhaustive analytical and numerical analysis of different properties of the model becomes possible. In what follows we analyze a stability of various spin–Peierls phases at zero temperature in the presence of external field. For this purpose we consider a nonuniform spin2 isotropic XY chain in a transverse field defined by the Hamiltonian