Entanglement features of Floquet random and fully random unitary quantum circuits

We study the entanglement dynamics for Floquet random and fully random unitary circuits. The Floquet circuit consists of an on-site Haar random layer alternating with a nearest neighbor interaction layer. In the limit where the local Hilbert space dimension q is large, we show an emergent Ising symmetry and obtain an analytical expression for short time periods via the transfer matrix method. Based on our short time result, we promote the "entanglement feature" to an operator formalism and derive a diffusion equation for the entanglement dynamics at long times. The similar functional form of the corresponding diffusion operators implies a universal thermalization behavior in Floquet random and fully random unitary circuits.

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