Entanglement propagation and dynamics in non-additive quantum systems

Abstract

The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and transport, due to the breakdown of the common mechanism based on excitations propagation and confinement. Here, we describe the dynamics of the entanglement entropy in many-body quantum systems with diverging long-range two body potentials. While in the strict thermodynamic limit entanglement dynamics is shown to be suppressed, a rich mosaic of novel scaling regimes is observed at intermediate system sizes, due to the possibility to trigger multiple resonant modes in the global dynamics. Quantitative predictions on the shape and timescales of entanglement propagation are made, paving the way to the observation of these phases in current quantum simulators. This picture is connected and contrasted with the case of local many body systems subject to Floquet driving.

Quantum heat engine with long-range advantages

“…The thermodynamic advantage demonstrated in the present analysis shall become even more prominent in the so-called strong long-range regime (α 1,2 < 1), in which the system loses additivity. However, the thermalization of the system on an accessible time scale is not guaranteed in this regime, as the fermionic dispersion relation becomes gapped [57,58], thus allowing for the presence of long-lived prethermal and quasi-stationary phases [83]. Further investigation is thus needed in order to understand this regime.…”

“…Moreover, long-range interactions are known to alter the universal behavior of critical systems at and out of equilibrium, generating a wide range of unprecedented phenomena. These include novel form of dynamical phase transitions [48,49], defect formation [48,[50][51][52], anomalous thermalization [53], information spreading [54][55][56] and metastable phases [57,58], whose features have no-counterpart in systems with short-range interactions.…”

High-order time crystal phases and their fractal nature

“…Indeed, while LR interactions are known to alter the universal behaviour of critical systems at equilibrium [36,37], they also generate a wide range of unprecedented outof-equilibrium phenomena. These include novel form of dynamical phase transitions [38,39], defect formation [38,[40][41][42], anomalous thermalization [43], information spreading [44][45][46] and metastable phases [47,48], whose features have no-counterpart in local dynamics.…”

“…As shown in Refs. [47,48] the out-of-equilibrium dy-namics of the system for any α < d is expected to converge to the α = 0 case in the thermodynamic limit, so that in the following we are going to set α = 0 and N α = N . The dynamics under consideration is the one of the kicked Ising model, in which the driving is given by…”

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

“…The previous discussion changes and becomes more involved for systems with long-range couplings [2,37,38]. Indeed the prominent collective character of such non-local systems promotes entanglement spreading and leads to novel forms of equilibrium and dynamical scaling, which cannot be observed in traditional systems with local interactions [39][40][41]. In particular, the anomalous scaling of entanglement in the presence of long-range couplings has recently attracted great interest in the context of the so-called measurement-induced transitions [42][43][44][45][46][47][48].…”