Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing

TL;DR

This paper investigates how long-range hopping and pairing in a Kitaev chain influence entanglement entropy, revealing diverse scaling behaviors including logarithmic, fractal, and volume-law regimes depending on system parameters.

Contribution

It provides a comprehensive analytical and numerical analysis of entanglement scaling in long-range Kitaev chains, uncovering new regimes of entanglement behavior.

Findings

Identification of logarithmic, fractal, and volume-law entanglement regimes

Dependence of entanglement scaling on chemical potential and decay strength

Rich phenomenology due to non-local interactions

Abstract

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.