SciPost Phys. 8, 068 (2020) ·
published 28 April 2020

· pdf
We provide exact results for the dynamics of localoperator entanglement in
quantum circuits with twodimensional wires featuring ultralocal solitons, i.e.
singlesite operators which, up to a phase, are simply shifted by the time
evolution. We classify all circuits allowing for ultralocal solitons and show
that only dualunitary circuits can feature moving ultralocal solitons. Then,
we rigorously prove that if a circuit has an ultralocal soliton moving to the
left (right), the entanglement of local operators initially supported on even
(odd) sites saturates to a constant value and its dynamics can be computed
exactly. Importantly, this does not bound the growth of complexity in chiral
circuits, where solitons move only in one direction, say to the left. Indeed,
in this case we observe numerically that operators on the odd sublattice have
unbounded entanglement. Finally, we present a closedform expression for the
localoperator entanglement entropies in circuits with ultralocal solitons
moving in both directions. Our results hold irrespectively of integrability.
SciPost Phys. 8, 067 (2020) ·
published 28 April 2020

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The entanglement in operator space is a well established measure for the
complexity of the quantum manybody dynamics. In particular, that of local
operators has recently been proposed as dynamical chaos indicator, i.e. as a
quantity able to discriminate between quantum systems with integrable and
chaotic dynamics. For chaotic systems the localoperator entanglement is
expected to grow linearly in time, while it is expected to grow at most
logarithmically in the integrable case. Here we study localoperator
entanglement in dualunitary quantum circuits, a class of "statistically
solvable" quantum circuits that we recently introduced. We identify a class of
"completely chaotic" dualunitary circuits where the localoperator
entanglement grows linearly and we provide a conjecture for its asymptotic
behaviour which is in excellent agreement with the numerical results.
Interestingly, our conjecture also predicts a "phase transition" in the slope
of the localoperator entanglement when varying the parameters of the circuits.
SciPost Phys. 7, 005 (2019) ·
published 8 July 2019

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We investigate the dynamics of bipartite entanglement after the sudden
junction of two leads in interacting integrable models. By combining the
quasiparticle picture for the entanglement spreading with Generalised
Hydrodynamics we derive an analytical prediction for the dynamics of the
entanglement entropy between a finite subsystem and the rest. We find that the
entanglement rate between the two leads depends only on the physics at the
interface and differs from the rate of exchange of thermodynamic entropy. This
contrasts with the behaviour in free or homogeneous interacting integrable
systems, where the two rates coincide.