  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 non-dimerized 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 (DMRG) 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.
