Spin-Peierls Transition with Competing Interactions

The one-dimensional spin-1/2 Heisenberg antiferromagnet which has next-nearest-, as well as nearest-neighbor exchange interaction and couples to the lattice distortion is investigated. The next-nearest-neighbor interaction is shown to result from the non-adiabaticity of the lattice distortion or the itineracy of electrons. The groundstate of this system is studied by the renormalization group method. In the absence of the coupling to the lattice distortion, the phase diagram consists of three states, i.e., the spin-fluid, the dimer and the Néel state, in essential agreement with Haldane, while in its presence, there are two states, the spin-Peierls and the Néel state. The energy gain due to the lattice distortion is estimated by the self-consistent harmonic approximation.