Quantum Quenches Demonstrate Universal Equilibration Dynamics after Global Disturbances

The behaviour of quantum systems following a sudden disturbance, known as a quantum quench, remains a fundamental question in physics, and recent work by Vincenzo Alba, Sanam Azarnia, Gianluca Lagnese, and Federico Rottoli from the University of Pisa and the Jožef Stefan Institute sheds new light on this process. The researchers demonstrate that the distribution of energy levels within these disturbed systems exhibits a surprising degree of universality, meaning its characteristics become independent of the specific details of the initial system. This achievement reveals that the long-term evolution after a quench depends on only a few key properties, specifically those captured by quantities called Rényi entropies, and predicts two distinct scenarios for how energy levels arrange themselves. By validating these findings across a range of established quantum models, including free-fermion chains and Bethe ansatz solvable spin models, the team provides a significant step towards understanding the general principles governing the relaxation of quantum systems after disruption.

This work demonstrates that, in an appropriate scaling limit, the lower part of the entanglement spectrum exhibits universality. In this limit and at asymptotically long times, the distribution of the entanglement spectrum depends on two parameters which can be determined from the Rényi entropies. The research reveals two typical scenarios, the first of which shows the distribution of entanglement spectrum levels resembling that describing the ground-state entanglement spectrum in Conformal Field Theories. The second scenario demonstrates that the lower levels of the entanglement spectrum are highly degenerate, and their distribution is given by a series of Dirac deltas. The findings are benchmarked against existing theoretical frameworks.

Entanglement Evolution After a Quantum Quench

This is a comprehensive collection focused on quantum information theory, many-body physics, and the dynamics of entanglement in interacting quantum systems, particularly after a quantum quench. A central theme is the study of how quantum systems evolve after a sudden change in their Hamiltonian, a fundamental problem in non-equilibrium statistical mechanics. The primary focus is on understanding how entanglement changes over time following a quench, including measurements of entanglement entropy and analysis of the entanglement spectrum. Researchers also explore operator entanglement, a concept that considers entanglement in the space of operators, and utilize measures like negativity and Rényi entanglement to characterize mixed states.

Many papers focus on integrable quantum systems, which possess an infinite number of conserved quantities, making them solvable and providing a benchmark for understanding more complex systems. Theoretical frameworks like Generalized Hydrodynamics describe the non-equilibrium dynamics of these systems, often framed in terms of quasiparticle propagation and interaction. Numerical techniques, such as Matrix Product States and Time-Evolving Matrix Product States, are used to simulate the time evolution of quantum systems, particularly in one dimension. Specific models, including the XXZ spin chain, the transverse field Ising chain, and the Rule 54 cellular automaton, are frequently studied.

Researchers employ tools like the quench action and string-charge duality to solve integrable models, and utilize methods such as the Density Matrix Renormalization Group and Time-Dependent Matrix Product Ansatz for simulations. Investigations cover dynamical quantum phase transitions, inhomogeneous quenches, the Memba effect, and quantum Floquet-Thouless pumps, all examining how correlation functions and order parameters evolve after a quench. Recent trends include a growing interest in operator entanglement, entanglement Hamiltonians, higher-dimensional systems, and applications to real materials. This collection represents an active area of research aiming to understand entanglement evolution in complex quantum systems and develop new theoretical and numerical methods for studying non-equilibrium dynamics.

Eigenvalue Distribution Reveals Quantum Equilibration Universality

Scientists investigated the distribution of eigenvalues within the reduced density matrix following a global quantum quench, revealing a surprising degree of universality in the system’s behavior. The research demonstrates that, in a specific scaling limit, the lower portion of the spectrum exhibits predictable characteristics, dependent on only two parameters determined from Rényi entropies. Experiments revealed two distinct scenarios governing the distribution of these spectrum levels, providing new insight into quantum equilibration. In the first scenario, the distribution closely resembles the ground-state spectrum observed in Conformal Field Theories, suggesting a deep connection between these theoretical frameworks and dynamic quantum systems.

Conversely, the team discovered that in the second scenario, the lower levels of the spectrum become highly degenerate, manifesting as a series of Dirac delta functions, indicating a fundamentally different organization of entanglement. The study benchmarked these analytical results against several established models, including free-fermion chains and Bethe ansatz solvable spin models, confirming the robustness of the findings. Measurements of Rényi entropies show a volume-law scaling in the long-time regime, mirroring the thermodynamic entropy of the system’s steady state, and a linear increase during the short-time regime, providing a detailed picture of entanglement growth. This breakthrough reconstructs the full distribution of eigenvalues of the reduced density matrix, building upon previous research on ground-state entanglement spectra in Conformal Field Theories, and delivers a new understanding of how entanglement spreads in quantum systems.

Eigenvalue Distributions Reveal Entanglement and Universality

This research presents a detailed investigation into the distribution of eigenvalues within the reduced density matrix following a rapid change, or quench, in a quantum system, revealing fundamental properties of how these systems evolve towards equilibrium. Scientists demonstrate that, under specific conditions, the lower portion of this eigenvalue spectrum exhibits universal behaviour, meaning its characteristics are independent of the specific details of the system. Importantly, the distribution of these eigenvalues depends on parameters directly linked to Rényi entropies, quantities that measure entanglement between different parts of the system. The team identified two distinct scenarios governing this eigenvalue distribution, both supported by benchmarking against several established models.

In some cases, the distribution closely resembles that found in the ground state of conformal field theories, a well-understood class of quantum systems. Alternatively, the lower levels of the spectrum can become highly concentrated, exhibiting a distribution resembling a series of discrete energy levels. Further research could focus on extending these findings to more complex systems and investigating the dynamics of the full entanglement spectrum, potentially offering deeper insights into the process of thermalization in isolated quantum systems.