Novel quantum state in a high-spin chain created by the spontaneous symmetry breaking

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In this project, we have explored the finite-field ground states of a variety of high-spin (mainly, S=1) chains, employing numerical and analytical methods. The main results which we have obtained are summarized as follows.1.One-Dimensional S=1 Ferromagnetic-Antiferromagnetic Bond-Alternating Chain with Uniaxial Single-IonAnisotropy EnergiesWe have examined the finite-field ground state of the present system by means of the density-matrix renormalization-group method, and clarified that two kinds of 1/2-plateaux (the magnetization plateau at the half of the saturation magnetization) appear in the ground-state magnetization curve. Furthermore, employing the level spectroscopy method based on the exact diagonalization method for finite-size systems, we have determined the 1/2-magnetization plateau phase diagram on the plane of the interaction parameters and also the magnetization phase diagram on the magnetic field versus interaction parameter plane.2.Anisotropic One-Dimensional S=1 Anti … More ferromagnetic ChainWe have studied, by means of the density-matrix renormalization-group method, the finite-field ground state of the one-dimensional antiferromagnetic chain with Ising-type anisotropic exchange interactions and uniaxial single-ion anisotropy energies. The obtained results are : i)The magnetization jump anomaly corresponding to the first-order phase transition appears in the ground-state magnetization curve, and ii)the commensurate-incommensurate phase transition corresponding to the second-order one takes place in the finite-field ground state.3.One-Dimensional S=1 Chain with Bond-Alternating Nearest-Neighbor and Uniform Next-Nearest-Neighbor InteractionsFirst, we have calculated the dispersion relation of the spin-wave excitation from the ferromagnetic state, from the result of which we have rigorously determined the phase boundary line between the ferromagnetic and nonmagnetic singlet phases on the plane of the interaction parameters. Then, we have calculated, using the density-matrix renormalization-group method, the ground-state magnetization curve in the parameter region where the non-magnetic singlet phase is stable, and found that the 1/2-plateau appears in the magnetization curve. Finally, we have determined the 1/2-plateau phase diagram on the plane of the interaction parameters by applying the level spectroscopy method. Less