The Mpemba effect, where a state prepared farther from equilibrium relaxes faster to equilibrium than one prepared closer, has a quantum counterpart where relaxation is resolved by conserved charge. However, the fate of the quantum Mpemba effect in systems with long-range interactions remains an open question. Here, we study the quantum Mpemba effect in long-ranged, U(1)-symmetric random unitary circuits. Using annealed Rényi-2 entanglement asymmetry computed via replica tensor networks and exact diagonalization, we track the symmetry restoration from three types of tilted product states: ferromagnetic, antiferromagnetic, and ferromagnetic with a central domain wall. The quantum Mpemba effect is present for tilted ferromagnetic states at all interaction ranges, but absent for tilted antiferromagnetic states, and it occurs for the domain-wall state only in effectively short-ranged circuits, where the Mpemba time $t_{\mathrm{M}}$ is found to scale with the subsystem size $N_A$ as $t_{\mathrm{M}}\sim N_A^z$, with the dynamical exponent $z=min(\alpha -1,2)$. These results reveal how the quantum Mpemba effect is governed by the interplay between interaction range and initial-state charge bias in long-ranged chaotic systems.

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• Entanglement entropy
• Quantum circuits
• Quantum many-body systems
• Numerical approximation & analysis