Logarithmic, fractal and volume-law entanglement in a Kitaev chain with long-range hopping and pairing

Thanks to their prominent collective character, long-range interactions promote information spreading and generate forms of entanglement scaling, which cannot be observed in traditional systems with local interactions. In this work, we study the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range hopping and pairing couplings decaying with a power law of the distance. We provide a fully-fledged analytical and numerical characterization of the asymptotic growth of the ground state entanglement in the large subsystem size limit, finding that the truly non-local nature of the model leads to an extremely rich phenomenology. Most significantly, in the strong long-range regime, we discovered that the system ground state may have a logarithmic, fractal, or volume-law entanglement scaling, depending on the value of the chemical potential and on the strength of the power law decay.

Automated summary

In this study, we investigate the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range hopping and pairing couplings. We find that the system exhibits an extremely rich phenomenology due to its truly non-local nature. In the strong long-range regime, we observe logarithmic, fractal, or volume-law entanglement scaling depending on the values of the chemical potential and power law decay strength.