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The European Physical Journal B

Dimerized phase and entanglement in the one-dimensional spin-1 bilinear biquadratic model

Ai Min Chen, Su Yao, Honglei Wang

Published Oct 1, 2015• 1 citation
Publisher
DOI
10.1140/epjb/e2015-60391-y

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The excitation spectra of the T=0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the newly defined center fluctuation operator in the one-dimensional S=1 Heisenberg model wi th isotropic bilinear (Jcos⁡θ)(J\cosθ)(Jcosθ) and biquadratic (Jsin⁡θ)(J\sinθ)(Jsinθ) exchange are investigated via the recursion method for systems with up to N=18 site s over the predicted range, $-π/4
We investigate the effect of the Berry phase on quadrupoles that occur, for example, in the low-energy description of spin models. Specifically, we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a nondimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory and then verify the predictions using large scale density-matrix renormalization group simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.
We investigate the isotropic two-leg S=S=S=12\frac{1}{2}21​ ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians that have a matrix-product wave function as an exact ground state. We demonstrate that a smooth change of parameters leads one from the S=S=S=12\frac{1}{2}21​ dimer and Majumdar-Ghosh chains to the S=1S=1S=1 chain with biquadratic exchange, which proves that these model systems are in the same phase. The family of Hamiltonians also includes a set of models of isotropic S=S=S=12\frac{1}{2}21​ chains with only bilinear nearest- and next-nearest-neighbor interactions. The ground state for these models becomes unstable at a line of first-order phase transitions to the ferromagnetic state.