Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results

The growth of the entanglement between two disjoint intervals and its complement after a quantum quench is regarded as a dynamical chaos indicator. Namely, it is expected to show qualitatively different behaviours depending on whether the underlying microscopic dynamics is chaotic or integrable. So far, however, this could only be verified in the context of conformal field theories. Here we present an exact confirmation of this expectation in a class of interacting microscopic Floquet systems on the lattice, i.e., dual-unitary circuits. These systems can either have <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>z</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi></mml:math> or a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">super extensive</mml:mtext></mml:mrow></mml:math> number of conserved charges: the latter case is achieved via fine-tuning. We show that, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:math> all dual unitary circuits on qubits and for a large family of dual-unitary circuits on qudits the asymptotic entanglement dynamics agrees with what is expected for chaotic systems. On the other hand, if we require the systems to have conserved charges, we find that the entanglement displays the qualitatively different behaviour expected for integrable systems. Interestingly, despite having many conserved charges, charge-conserving dual-unitary circuits are in general not Yang-Baxter integrable.