Universal dynamics of quantum phase transitions with fractional long-range interactions

arXiv:2611.05273v1 Announce Type: new Abstract: The complete statistical characterization of defects generated in a quantum phase transition has mostly been studied in exactly solvable models, and remains little explored in nonintegrable systems such as long-range interacting spin chains. We characterize the full defect counting statistics in a nonintegrable long-range spin chain, the fractional Ising model, by time-dependent variational-principle simulations within the matrix-product-state and matrix-product-operator formalism. Fractional interactions capture emergent multiscale correlations and long-range effects in nature, governed by the order of the underlying fractional derivative. Such couplings can be approximated on existing quantum simulation platforms, where the full defect statistics can be measured. The defect number cumulants follow power laws in the driving time, with exponents that vary continuously with the fractional order. At low fractional order, deep in the long-range regime, the mean defect number decays more slowly than predicted by the Kibble-Zurek mechanism (KZM), while at intermediate order the KZM holds with the numerically extracted many-body critical exponents. At large fractional order, the exactly solvable free-fermion limit of the model becomes progressively more accurate towards the short-range limit. We derive exact bounds on the kink-number cumulants and on the kink-kink correlations, implying an exact Gaussian limiting distribution for large system sizes. In the many-body simulations, however, kinks are more correlated, consistent with the confinement of domain walls, and these bounds are violated in the long-range regime, also in the bulk of the chain. Nevertheless, the kink distribution still approaches a Gaussian for large defect numbers, with proportionality partially broken between the cumulants.