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

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.

Time Crystal Synthon: The Way to Integrate Cascade Reactions for Advancing Multistep Flow Synthesis

“…Besides integrating the cascade reactions in forming a cascade of cyclic reactions, other time-crystals of different fields can also be artificially integrated to form the polytimecrystal [15,[41][42][43]. However, we must ensure that one product of the system (time-crystal) can be consumed by another system (time-crystal) without any external effort.…”

“…However, we must ensure that one product of the system (time-crystal) can be consumed by another system (time-crystal) without any external effort. The coupling of two (spin-1/2 systems) or more (ultracold atoms or trapped ions) time-crystals can be found in the atomic or subatomic systems' [41] Kitaev chain [42]. Fractal time-crystals can also be found in various biological systems like the brain [15], protein, microtubule, and neurons [43].…”

“…Fractal time-crystals can also be found in various biological systems like the brain [15], protein, microtubule, and neurons [43]. By extrapolating the concept of coupling timecrystals [15,[41][42][43], we can construct the cascade reaction cycle or fractal reaction cycles.…”

Electrical, thermal and thermoelectric transport in open long-range Kitaev chain

“…In recent years, an extended version, namely the long-range Kitaev (LRK) chain, has become significant from both theoretical and experimental points of view. Long-range chain, which allows pairing and hopping terms to couple electrons from non-adjacent sites with strength decaying algebraically with the distance between the sites, shows stability against external perturbations [16][17][18][19][20][21]. Moreover, the long-range interactions induce novel correlations and entanglement behavior [22], delocalization of Majorana states in 1D LRK chain [23].…”