Entanglement barriers in dual-unitary circuits

After quantum quenches in many-body systems, finite subsystems evolve nontrivially time, eventually approaching a stationary state. In typical situations, the reduced density matrix of given subsystem begins and ends this endeavor as low-entangled vector space operators. This means that if its entanglement operator initially grows (which is generically case), it must decrease, describing barrier-shaped curve. Understanding shape ``entanglement barrier'' interesting for three main reasons: (i) quantifies dynamics (open) subsystem; (ii) gives information on approximability by product operators; (iii) shows qualitative differences depending type undergone system, signaling chaos. Here we compute exactly barriers described different R\'enyi entropies after dual-unitary circuits initialized class solvable states (MPS)s. We show that, free (SWAP-like) circuits, entropy behaves rational conformal field theories (CFT)s. On other hand, completely chaotic holographic CFTs, exhibiting longer barrier drops rapidly when thermalizes. Interestingly, spectrum nontrivial case. Higher behave an increasingly similar way to such are identical limit infinite replicas (i.e., so called min-entropy). also upon increasing bond dimension MPSs, maintains same shape. It simply shifts left accommodate larger initial entanglement.