Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

摘要

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO4 equivalent to LiSbCuO4 and Rb2Cu2Mo3O12, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM) (J(1), J'(1) < 0) and next-nearest-neighbor antiferromagnetic (J(2) > 0) couplings. Using the density-matrix renormalization group technique and spin-wave theory, we find a first-order transition between a fully polarized FM and an incommensurate spiral state at 2 alpha = beta/(1 + beta), where alpha is the frustration ratio J(2)/|J(1)| and beta the degree of dimerization J'(1)/J(1). In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO4. For larger alpha, corresponding to Rb2Cu2Mo3O12, and smaller beta there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence-bond solid state with substantial spin gaps.