Abstract
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of "maximally chaotic", periodically driven, quantum spin chains. Specifically, we consider the so called "self-dual" kicked Ising chains initialised in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the models considered are maximally chaotic: their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so called "minimal cut" bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel "duality-based" numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is non-integrable.
Highlights
Entanglement is arguably the most distinctive feature of quantum mechanics
The evolution of the entanglement gives crucial information on how equilibrium statistical mechanics emerges from many-body quantum dynamics
We identify a class of separable initial states, homogeneous or arbitrarily modulated in space, from which the entanglement dynamics can be computed exactly for any nondisjoint bipartition
Summary
Entanglement is arguably the most distinctive feature of quantum mechanics. It generates special kinds of nonlocal correlations which can be present in quantum states but have no analogues in the classical realm. A candidate emerging naturally in our quest is the so-called kicked Ising model [58,59,60], which describes a classical Ising model in the presence of a longitudinal magnetic field and periodically kicked with a transverse-magnetic field This model is quantum chaotic in the sense that its spectral statistics are described by the circular orthogonal ensemble of random matrices [61], but, as we recently proved [56], at some specific points of its parameter space it allows for exact calculations. The thermodynamic limit is taken for fixed initial state and time-evolving Hamiltonian
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