Random Free-Fermionic Systems Exhibit Scrambling Without Chaos, Revealing Partial Crossover in Level-Spacing Ratio

The fundamental question of how information spreads and becomes scrambled within complex systems drives research across many scientific disciplines, and now, Ali Mollabashi, Mohammad-Javad Vasli, and colleagues at the Institute for Research in Fundamental Sciences are shedding new light on this process within a surprising context, integrable systems. Traditionally, scrambling, the rapid dispersal of information, has been linked to chaotic behaviour, but this team demonstrates that randomness alone can induce scrambling even when the underlying system maintains its inherent order. Their work reveals that introducing randomness into integrable free-fermionic models causes information to delocalize and exhibits characteristics, such as negative saturation in tripartite mutual information and a partial crossover in level-spacing statistics, reminiscent of chaotic systems, albeit to a lesser degree. This achievement establishes that randomness serves as a crucial, minimal ingredient for inducing information scrambling, challenging the conventional link between chaos and information dispersal and opening new avenues for understanding complex dynamics.

Entanglement Entropy and Many-Body Systems

This is a comprehensive collection of research covering quantum information, many-body physics, quantum chaos, and related areas. It encompasses core concepts, theoretical foundations, specific systems, and advanced topics, exploring entanglement entropy, its calculation, and its properties in various systems, with foundational work by researchers such as Casini, Huerta, Vidal, and Cardy. The research also investigates the connection between quantum chaos and the statistical properties of energy levels, building on the classic work of Bohigas, Giannoni, and Schmit. A key focus is on thermalisation and many-body localisation, particularly the crucial work of Oganesyan and Huse, which contrasts with the usual expectation of thermalisation in closed quantum systems.

The research also examines quantum quenches, sudden changes in the Hamiltonian, as a tool for understanding non-equilibrium dynamics, with significant contributions from Calabrese and Cardy. Mutual information and monogamy, explored by Hayden, Headrick, and Maloney, link entanglement to gravity and black hole physics. A large portion of the research focuses on free fermion systems and quadratic Hamiltonians, often exactly solvable, allowing for analytical calculations of entanglement entropy and other quantities, with central contributions from Lydzba, Rigol, and Vidmar. Researchers also investigate integrable systems, systems with an infinite number of conserved quantities, and their special properties, such as the lack of thermalisation and the existence of exact solutions.

The research extends to spin chains, with foundational work by Vidal, Latorre, and Rico, and the Sachdev-Ye-Kitaev (SYK) model, a solvable model of interacting fermions with connections to black holes and quantum gravity. Dual-unitary circuits, investigated by Foligno and Bertini, provide a simplified model for studying quantum dynamics. The Page curve, which describes the entanglement entropy of a subsystem, is a central theme, particularly in the context of black hole physics and the information paradox, with contributions from Bianchi, Hackl, and Vidmar. The Eigenstate Thermalisation Hypothesis (ETH), while not always explicitly mentioned, is implicitly present in many papers.

The research explores information scrambling, complexity, and the connections between entanglement, quantum information, and gravity, particularly in the context of the AdS/CFT correspondence. The work of Oganesyan and Huse is crucial in understanding how disorder can prevent thermalisation and lead to localised states. Key authors recurring throughout the research include P. Calabrese, a leading researcher in quantum quenches and entanglement entropy; M. Rigol, with extensive work on entanglement, thermalisation, and many-body localisation in quadratic Hamiltonians; L.

Vidmar, who collaborates extensively with Rigol; M. Huerta and H. Casini, with foundational work on entanglement entropy; V. Alba, researching quantum quenches and integrable systems; M. Bianchi, working on entanglement in free fermionic systems and the Page curve; and E.

Rico and J. I. Latorre, with early work on entanglement in spin chains. Overall, this collection represents a comprehensive and cutting-edge exploration of quantum information, many-body physics, and quantum chaos, focusing on the fundamental properties of entanglement, thermalisation, and localisation, and their connections to other areas of physics.

Randomness Induces Information Scrambling in Integrable Systems

This research demonstrates that even within integrable quantum systems, randomness can induce the scrambling of information, a process crucial to understanding black holes and quantum chaos. Scientists investigated free-fermionic models, systems typically lacking the chaotic behaviour associated with information scrambling, and introduced varying degrees of randomness into their local couplings. The team observed that the memory effect in entangled subsystems vanishes with sufficient randomness, indicating that information becomes delocalised throughout the system. Furthermore, the tripartite mutual information, a measure of correlation, exhibited negative saturation values reminiscent of chaotic systems, though to a lesser extent, suggesting weaker scrambling in these integrable models.

Analysis of the spectral properties revealed a ramp structure in the spectral form factor, a characteristic often associated with chaotic systems, despite the underlying integrability. Notably, the level-spacing ratio, which describes the distribution of energy levels, transitioned from Poisson-like to Wigner-Dyson-like behaviour as the range of random couplings broadened, mirroring a shift towards chaotic characteristics. However, this transition remained partial, and the researchers acknowledge that a comprehensive analysis of extremely narrow coupling ranges requires further investigation. These findings establish that randomness serves as a minimal ingredient for inducing information scrambling, even in systems not inherently chaotic, and offer valuable insight into the interplay between integrability, randomness, and quantum information processing.