Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

Abstract

We derive the quasiparticle picture for the fermionic logarithmic negativity in a tight-binding chain subject to gain and loss dissipation. We focus on the dynamics after the quantum quench from the fermionic Néel state. We consider the negativity between both adjacent and disjoint intervals embedded in an infinite chain. Our result holds in the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed. Additionally, we consider the weakly-dissipative limit, in which the dissipation rates are inversely proportional to the size of the intervals. We show that the negativity is proportional to the number of entangled pairs of quasiparticles that are shared between the two intervals, as is the case for the mutual information. Crucially, in contrast with the unitary case, the negativity content of quasiparticles is not given by the Rényi entropy with Rényi index 1/21/2, and it is in general not easily related to thermodynamic quantities.

Zeno crossovers in the entanglement speed of spin chains with noisy impurities

“…We also observe that, increasing τ prolongs the heating regime and attenuates the Zeno suppression of noise averaged entanglement spreading in the Zeno regime. All our results are qualitatively explained by employing the quasi-particle picture of entanglement spreading similar to the entanglement spreading mechanism reported in [39,40,[57][58][59].…”

“…In particular we focus on the S ent (t) = S η ent (t) η of the spins between site l = 0 and site m = L. We observe a linear growth of the S ent (t) (see figure 2) as expected, and a non-monotonous behaviour of the Ṡent = ∂ t S ent (t) as a function of the coupling κ to the dissipative impurity (see figure 3). Both observations can be qualitatively explained with the quasi-particle picture of entanglement spreading [39,40,48,[56][57][58][59].…”

Rényi negativities in non-equilibrium open free-boson chains

“…In the paper [13,14], the authors first propose the quasi-particle picture in this context. In paper [15,16], people explore the temporal evolution of fermionic logarithmic negativity in a free fermion chain. However, the quench dynamics of negativity in bosonic open quantum systems have not been studied before.…”

“…Due to its complications, we will need a more sophisticated method to obtain the dynamics of entanglement. We are interested in the weak-dissipation hydrodynamic limit: t, l → ∞,γ ± → 0 with t/l and γ ± t keep fixed [14,15,21].…”

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

“…The boundaries of this picture must, however, be expanded for this purpose: the stationary states of open systems may deviate drastically in their characteristics from equilibrium states, as can be usefully captured by the long-range correlations that they tend to exhibit [4][5][6]. For quantum systems, an obvious emphasis should be put on analyzing measures of many-body entanglement [7,8], as they embody specifically the non-classical aspect of this departure from the familiar landscape of equilibrium [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The promise of the entanglement perspective is underlined by the significant achievements that it has already produced in the classification of quantum phases, of topological phases, and of dynamical traits of closed quantum systems after a non-equilibrium quench [23][24][25][26][27][28].…”