Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains

Abstract

We present a numerical study of the magnetization process of frustrated quantum spin-$S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-$S$ chains with $S>1∕2$. Similar to the case of $S=1∕2$, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-$S=1$, $3∕2$, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-$3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-$3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.