Magnetization properties of some quantum spin ladders

Abstract

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-½ ladder, and a two-legged spin-½ ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-½ chain in a magnetic field; the second-order terms give corrections to the XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.