Quantum Mpemba Effect in Random Circuits

Quantum Mpemba Effect in Random Circuits

May 24, 2024 | Xhek Turkeshi, Pasquale Calabrese, Andrea De Luca
The study investigates the quantum Mpemba effect in random circuits with a $U(1)$ conservation law, focusing on the dynamics of charge-preserving systems. The authors combine numerical simulations and analytical methods to explore the entanglement asymmetry as a signature of the Mpemba effect. They find that initial states with higher symmetry breaking (tilted ferromagnets) exhibit faster symmetry restoration and reach the grand-canonical ensemble more quickly compared to states with lower symmetry breaking (tilted antiferromagnets). The Mpemba effect is absent for short timescales ($t \ll N_A$) but becomes significant at larger times ($t \sim N_A$), where the dynamics are described by operator spreading. The analysis is based on minimal principles of locality, unitarity, and symmetry, providing insights into the emergence of Mpemba physics in generic systems, including Hamiltonian and Floquet quantum circuits. The findings highlight the importance of initial state asymmetry in the relaxation dynamics of quantum systems.The study investigates the quantum Mpemba effect in random circuits with a $U(1)$ conservation law, focusing on the dynamics of charge-preserving systems. The authors combine numerical simulations and analytical methods to explore the entanglement asymmetry as a signature of the Mpemba effect. They find that initial states with higher symmetry breaking (tilted ferromagnets) exhibit faster symmetry restoration and reach the grand-canonical ensemble more quickly compared to states with lower symmetry breaking (tilted antiferromagnets). The Mpemba effect is absent for short timescales ($t \ll N_A$) but becomes significant at larger times ($t \sim N_A$), where the dynamics are described by operator spreading. The analysis is based on minimal principles of locality, unitarity, and symmetry, providing insights into the emergence of Mpemba physics in generic systems, including Hamiltonian and Floquet quantum circuits. The findings highlight the importance of initial state asymmetry in the relaxation dynamics of quantum systems.
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[slides and audio] Quantum Mpemba Effect in Random Circuits