Anomalous fractional quantization in the kagomelike Heisenberg ladder: Emergence of the effective spin-1 chain

Abstract

We study a Kagome-like spin-1/2 Heisenberg ladder with competing ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions. Using the density-matrix renormalization group based calculations, we obtain the ground state phase diagram as a function of the ratio between the FM and AFM exchange interactions. Five different phases exist. Three of them are spin polarized phases; an FM phase and two kinds of ferrimagnetic (FR) phases (referred to as FR1 and FR2 phases). The spontaneous magnetization per site is m = 1/2, 1/3, and 1/6 in the FM, FR1, and FR2 phases, respectively. This can be understood from the fact that an effective spin-1 Heisenberg chain formed by the upper and lower leg spins has a three-step fractional quantization of the magnetization per site as m = 1, 1/2, and 0. In particular, an anomalous "intermediate" state m = 1/2 of the effective spin-1 chain with the reduced Hilbert space from SU(3) to SU(2) symmetry is highly unexpected in the context of conventional spin-1 physics. The remaining two phases are spin-singlet phases with translational symmetry breaking in the presence of valence bond formations. One of them is octamer-siglet phase with a spontaneous octamerization long-range order of the system, and the other is period-4 phase characterized by the magnetic superstructure with a period of four structural unit cells. In these spin-singlet phases, we find the coexistence of valence bond structure and gapless chain. Although this may be emerged through the order-by-disorder mechanism, there can be few examples of such a coexistence.