Universality of the Negativity in the Lipkin–Meshkov–Glick Model

The numerical study conducted in the previous chapter raises several questions concerning universal properties of negativity of noncomplementary regions of spins at a continuous quantum phase transition. Will this critical quantity diverge in the thermodynamic limit? Does negativity exhibit universality? If so, can its scaling features be related to known exponents of the underlying model? Extrapolation of numerical results towards the thermodynamic may lead to rather misleading conclusions, and therefore the study of the preceding chapter can merely be considered as a hint towards universal features and scaling properties of negativity in the truly macroscopic system. The inherent complexity of the 1D models studied there has so far prevented a detailed analytical study. We argued that even if the structure of the ground state wave-function is known, it is not implied that negativity assumes a closed-form expression and, hence, its evaluation turns out to be intractable for large systems.

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