Variational and density-matrix renormalization-group studies of the frustrated antiferromagnetic Heisenberg S=1 quantum spin chain

摘要: In this paper we study a frustrated antiferromagnetic isotropic Heisenberg S=1 quantum spin chain H=${\ensuremath{\sum}}_{\mathrm{i}}$${\mathbf{S}}_{\mathrm{i}}$${\mathbf{S}}_{\mathrm{i}+1}$+\ensuremath{\alpha}${\ensuremath{\sum}}_{\mathrm{i}}$${\mathbf{S}}_{\mathrm{i}}$${\mathbf{S}}_{\mathrm{i}+2}$, using variational ansatz starting from valence bond states and the density-matrix renormalization group. We find both methods to give results in very good qualitative quantitative agreement, which clarify phase diagram as follows: At ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{D}}$=0.284(1), there is disorder point of first kind, marking onset incommensurate spin-spin correlations chain. ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{L}}$=0.3725(25) Lifshitz point, at excitation spectrum found develop particular doubly degenerate structure. These points are remnants transition spiral order classical ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{T}}$=0.7444(6) first-order an Affleck-Kennedy-Lieb-Tasaki (AKLT) characterized by nonvanishing string can be understood next-nearest-neighbor generalization AKLT model. transition, parameter shows (to numerical precision) discontinuous jump 0.085 zero; correlation length gap finite transition. The problem edge open chains discussed length.