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We study the level spacing statistics of three spin-1 models in onedimension, they are the Haldane chain, dual model which is obtained by Haldanechain under the Kennedy-Tasaki transformation and the combination of the firsttwo models which contains a solvable self-dual point. Although the first twomodels are unitary equivalent, their symmetries are different and this leads todifferent level spacing statistics in these two models. Concretely, the levelspacing in the Haldane chain obeys random matrix theory statistics, while thedual model shows non-random matrix theory statistics. This example shows thatthe level spacing statistics in two unitary equivalent systems can bedifferent. We find that the non-random matrix theory statistics in the dualmodel can be ascribed to a non-local hidden symmetry. Under perturbations thatremove the hidden symmetry, the dual model shows random matrix theorystatistics. For the last model, we observe a crossover from chaotic tointegrable around the self-dual point.

Level spacing statistics of the Haldane chain and its Kennedy-Tasaki dual