EMERGENT PHENOMENA FROM SPIN DEGREES OF FREEDOM IN LOW-DIMENSIONAL SYSTEMS

Abstract

We study emergent phenomena that occur in low dimensional spin and electronic systems, especially those related to spin degrees of freedom. In frustrated ferromagnetic spin-1 chains where the ferromagnetic nearest-neighbor coupling competes with the antiferromagnetic next-nearest-neighbor coupling, we analyze the ground state and its various correlation functions by using the density-matrix renormalization group. The double Haldane phase with ferromagnetic coupling shows incommensurate correlations of wavenumber $q$ with $0<q<\pi$ and transforms through a phase transition to the ferromagnetic phase. Such short-range correlations transform continuously into the ferromagnetic instability at the transition. The additional anisotropy in exchange interaction gives rise to a new disordered phase and a chirality phase in a wide region. We also compare the results with the spin-1/2 and classical spin systems, and discuss the string orders in the system.

We also investigate the magnetism on the edge of the Kane-Mele-Hubbard model. By means of the Hartree-Fock approximation we examine the nature of edge states in the presence of the Hubbard interaction in the Kane-Mele model. We compute local magnetizations of a nanoribbon with various widths. Phase diagram is obtained in the thermodynamic limit. It turns out that in-plane magnetic order survives at the edges in a wide range of the spin-orbit coupling. The variation of its characteristic length is shown to be closely related to the phase transition between topological insulator and antiferromagnetic insulator.