Variational and DMRG studies of the Frustrated Antiferromagnetic Heisenberg S=1 Quantum Spin Chain

Abstract

We study a frustrated antiferromagnetic isotropic Heisenberg $S=1$ chain using a variational ansatz and the DMRG. At ${\alpha }_D=0.284(1)$, there is a disorder point of the second kind, marking the onset of incommensurate correlations in the chain. At ${\alpha }_L=0.3725(25)$ there is a Lifshitz point, at which the excitation spectrum develops a doubly degenerate structure. These points are the quantum remnants of the transition from antiferromagnetic to spiral order in the classical frustrated chain. At ${\alpha }_T=0.7444(6)$ there is a first order phase transition from an AKLT phase to a next-nearest neighbor generalization of the AKLT model. At the transition, the string order parameter shows a discontinuous jump of 0.085 to 0; the correlation length and the gap are both finite at the transition. The problem of edge states in open frustrated chains is discussed at length.

37 pages, 14 figures, submitted to Phys.Rev. B

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• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Phase Diagram of the Spin-One Heisenberg System with Dimerization and Frustration

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