Entanglement dynamics after quantum quenches in generic integrable systems

By V. Alba, Pasquale Calabrese. 2017

222 citations recorded by the source corpus.

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

View Paper: https://www.semanticscholar.org/paper/2eadec3fbba9b9a9046bf9f5c186e8268a14f037

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Citations in the corpus

• Entanglement in a fermion chain under continuous monitoring (2018, background): “(17) of the initial state via the Yang-Yang entropy [44,51,52]: s(x, k, t) = s[n(x, k, t)] , (27) s[n] := − [n log2 n+ (1− n) log2(1− n)] .”
• Complexity and entanglement for thermofield double states (2018, methodology): “invariance by considering the system on an interval with, for example, Dirichlet instead of periodic boundary conditions. In g.23, we compare our numerical predictions with the Alba-Calabrese formula [74,75] adapted to our setup, i.e., with eq. (233). We observe a remarkably good t for the highest v”
• Diffusion in generalized hydrodynamics and quasiparticle scattering (2018, background): “12) is exactly the density per unit length of the GGE’s von Neumann entropy [147, 148].”