Quantum Mpemba Effect in Random Circuits

Quantum Mpemba Effect in Random Circuits

May 24, 2024 | Xhek Turkesi, Pasquale Calabrese, and Andrea De Luca
This paper investigates the quantum Mpemba effect in random circuits with a U(1) conservation law. The quantum Mpemba effect refers to the phenomenon where non-equilibrium systems relax faster when they are further from their equilibrium configuration. In the quantum realm, this effect is observed in the dynamics of closed systems, where it is characterized by symmetry and entanglement. The study focuses on charge-preserving random circuits on qudits, using entanglement asymmetry as a measure, and combines extensive numerical simulations with analytical mapping to a classical statistical mechanics problem. The research shows that certain classes of initial states, such as tilted ferromagnets, relax faster and reach the grand-canonical ensemble more quickly than others, like tilted antiferromagnets. This is attributed to the initial asymmetry of the states, with more asymmetric states restoring symmetry more rapidly. The analysis is based on minimal principles—locality, unitarity, and symmetry. The results highlight the emergence of Mpemba physics in generic systems, including Hamiltonian and Floquet quantum circuits. The study of far-from-equilibrium dynamics in quantum many-body systems has been a topic of significant interest, revealing foundational principles across theory and experiments. The quantum Mpemba effect (QME) has been associated with the anomalous relaxation dynamics of a quantum system with a conserved charge. The QME is non-universal, depending on the initial state, but its manifestations are widespread, as shown in studies on non-interacting and integrable systems and in trapped-ion experiments. The work clarifies the emergence of Mpemba phenomenology in chaotic quantum dynamics. It studies random circuits on d=2q dimensional qudits, which serve as minimal models for generic unitary evolution. The focus is on circuits with U(1) global symmetry and the evolution of asymmetry proxies as signatures of QME. Numerical simulations and analytical insights are used to demonstrate the QME in entanglement asymmetry at q=1 and q=2. The results show that the QME is absent for certain classes of initial states, such as tilted antiferromagnets. The study combines exact numerical methods, tensor network simulations, and analytical results. For finite qudits, the presence or absence of the QME is demonstrated for tilted ferromagnetic and antiferromagnetic initial states, with the Mpemba time scaling at least linearly with the subsystem size. The results are supported by insights from the q → ∞ limit, allowing clarification of the short-time behavior of the asymmetry via macroscopic fluctuation theory. At late times, the emergence of the Mpemba phenomenology for generic q is clarified using an operator spreading approach. The findings contribute to a deeper understanding of the quantum Mpemba effect in random circuits.This paper investigates the quantum Mpemba effect in random circuits with a U(1) conservation law. The quantum Mpemba effect refers to the phenomenon where non-equilibrium systems relax faster when they are further from their equilibrium configuration. In the quantum realm, this effect is observed in the dynamics of closed systems, where it is characterized by symmetry and entanglement. The study focuses on charge-preserving random circuits on qudits, using entanglement asymmetry as a measure, and combines extensive numerical simulations with analytical mapping to a classical statistical mechanics problem. The research shows that certain classes of initial states, such as tilted ferromagnets, relax faster and reach the grand-canonical ensemble more quickly than others, like tilted antiferromagnets. This is attributed to the initial asymmetry of the states, with more asymmetric states restoring symmetry more rapidly. The analysis is based on minimal principles—locality, unitarity, and symmetry. The results highlight the emergence of Mpemba physics in generic systems, including Hamiltonian and Floquet quantum circuits. The study of far-from-equilibrium dynamics in quantum many-body systems has been a topic of significant interest, revealing foundational principles across theory and experiments. The quantum Mpemba effect (QME) has been associated with the anomalous relaxation dynamics of a quantum system with a conserved charge. The QME is non-universal, depending on the initial state, but its manifestations are widespread, as shown in studies on non-interacting and integrable systems and in trapped-ion experiments. The work clarifies the emergence of Mpemba phenomenology in chaotic quantum dynamics. It studies random circuits on d=2q dimensional qudits, which serve as minimal models for generic unitary evolution. The focus is on circuits with U(1) global symmetry and the evolution of asymmetry proxies as signatures of QME. Numerical simulations and analytical insights are used to demonstrate the QME in entanglement asymmetry at q=1 and q=2. The results show that the QME is absent for certain classes of initial states, such as tilted antiferromagnets. The study combines exact numerical methods, tensor network simulations, and analytical results. For finite qudits, the presence or absence of the QME is demonstrated for tilted ferromagnetic and antiferromagnetic initial states, with the Mpemba time scaling at least linearly with the subsystem size. The results are supported by insights from the q → ∞ limit, allowing clarification of the short-time behavior of the asymmetry via macroscopic fluctuation theory. At late times, the emergence of the Mpemba phenomenology for generic q is clarified using an operator spreading approach. The findings contribute to a deeper understanding of the quantum Mpemba effect in random circuits.
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