Magnetization Properties of Some Quantum Spin Ladders

TL;DR

This paper investigates the magnetization behavior of quantum spin ladders, revealing specific magnetization plateaus and transition regions through numerical and analytical methods, advancing understanding of their quantum properties.

Contribution

It introduces a combined numerical and analytical approach to study magnetization plateaus and transitions in two types of quantum spin ladders, including new insights into their low-temperature properties.

Findings

Three-chain system exhibits a one-third saturation magnetization plateau.

Two-chain system shows zero and half saturation magnetization plateaus.

Transitions between plateaus are described by an XXZ spin-1/2 chain model.

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-1/2 ladder, and a two-legged spin-1/2 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-1/2 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.