1996/09/06 by A. K. Kolezhuk, A. Kolezhuk, R. Roth +3 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Algebraic structures and combinatorial models #Physics of Superconductivity and Magnetism #cond-mat
paper · pdf · doi:10.1103/physrevb.55.8928
37 pages, 14 figures, submitted to Phys.Rev. B
arxiv created 1996/09/06 · openalex publication_date 1997/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we study a frustrated antiferromagnetic isotropic Heisenberg S=1 quantum spin chain H=\ensuremath∑iSiSi+1+\ensuremathα\ensuremath∑iSiSi+2, using a variational ansatz starting from valence bond states and the density-matrix renormalization group. We find both methods to give results in very good qualitative and good quantitative agreement, which clarify the phase diagram as follows: At \mathrm\ensuremathαD=0.284(1), there is a disorder point of the first kind, marking the onset of incommensurate spin-spin correlations in the chain. At \mathrm\ensuremathαL=0.3725(25) there is a Lifshitz point, at which the excitation spectrum is found to develop a particular doubly degenerate structure. These points are the quantum remnants of the transition from antiferromagnetic to spiral order in the classical frustrated chain. At \mathrm\ensuremathαT=0.7444(6) there is a first-order phase transition from an Affleck-Kennedy-Lieb-Tasaki (AKLT) phase characterized by nonvanishing string order to a phase which can be understood as a next-nearest-neighbor generalization of the AKLT model. At the transition, the string order parameter shows (to numerical precision) a discontinuous jump of 0.085 to zero; 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.