Abstract
We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.
Highlights
While the states considered in Ref. [31] all relax to the Gibbs state with infinite temperature, here we show that exact results can be obtained for states relaxing to richer Gibbs ensembles
The reason appears to be connected to the fact that SA(α) have a stronger non-linear dependence on the state compared to the Von Neumann entanglement entropy
We showed that the entanglement dynamics from a class of solvable initial states is characterised by a certain tensor network and that, remarkably, the latter can be contracted exactly
Summary
The growth of entanglement is arguably the most universal phenomenon observed so far in studies of quantum many-body dynamics. A quantitative verification of these pictures and their predictive power in genuinely interacting systems, has proven to be a daunting task This is due to the fact that the out-of-equilibrium dynamics of interacting many-body quantum systems are generically too complicated to be characterised analytically and, the growth of entanglement provides a great limitation to the most efficient numerical methods at our disposal to treat quantum many-body systems [23]. For this reason, the benchmark provided by exact solutions in minimal solvable cases is of rare value. Some more technical points and proofs are reported in the two appendices
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