SciPost Phys. 8, 068 (2020) ·
published 28 April 2020
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· pdf
We provide exact results for the dynamics of local-operator entanglement in
quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e.
single-site 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 dual-unitary 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 closed-form expression for the
local-operator 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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· pdf
The entanglement in operator space is a well established measure for the
complexity of the quantum many-body 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 local-operator entanglement is
expected to grow linearly in time, while it is expected to grow at most
logarithmically in the integrable case. Here we study local-operator
entanglement in dual-unitary quantum circuits, a class of "statistically
solvable" quantum circuits that we recently introduced. We identify a class of
"completely chaotic" dual-unitary circuits where the local-operator
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 local-operator entanglement when varying the parameters of the circuits.
