Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

Abstract

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb-Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available. arXiv:1905.03206v3 [cond-mat.stat-mech]

Current Operators in Bethe Ansatz and Generalized Hydrodynamics: An Exact Quantum-Classical Correspondence

“…In our derivation, we assume that v eff ðλ j Þ > v eff ðλ k Þ whenever vðλ j Þ > vðλ k Þ. However, as natural as this requirement may seem, there can be situations where it does not hold [57]. In those cases, the quantum result remains valid, but the semiclassical picture cannot be applied.…”

Relaxation of bosons in one dimension and the onset of dimensional crossover

“…Within the non-degenerate regime, accurate predictions for the system can be obtained very efficiently using a simple molecular dynamics (MD) calculation [35][36][37][38]. MD is a wellestablished numerical tool of simulation of many-body dynamics in various fields such as physics of fluids or chemical physics.…”

Locally quasi-stationary states in noninteracting spin chains

“…On the one hand, universal properties have been uncovered within conformal field theories or, more generally, studying the time evolution of states sufficiently close to ground states of critical systems [23][24][25][26][27][28][29][30][31][32][33][34]; on the other hand, a generalised hydrodynamic description (GHD) has been shown to capture the behaviour of integrable systems at large scales [35,36]. GHD was originally based on a conjecture on the expectation value of the currents in stationary states and was tested by studying both entanglement entropies [37][38][39][40][41][42][43][44] and correlation functions [67][68][69][70][71][72][73]. Remarkably, the theory has been also verified in one experiment [74].…”