Non-local Ising Interactions Enable Complex Dynamics and Accelerated Quantum Chaos

The behaviour of complex magnetic systems, known as Ising models, forms a cornerstone of condensed matter physics, and understanding how these systems transition between order and chaos remains a significant challenge. Reza Pirmoradian, Elham Sadoogh, and Maryam Teymouri, along with colleagues at various institutions, now investigate this transition in both conventional and more complex, long-range interacting Ising models. Their work reveals that extending interactions beyond nearest neighbours dramatically increases the tendency towards chaotic behaviour, even with weak long-range connections, and accelerates the development of complex dynamics within the system. By employing sophisticated measures of energy level distribution and dynamical complexity, the team demonstrates a clear distinction between ordered and chaotic states, offering new insights into the fundamental mechanisms governing quantum chaos in magnetic materials and potentially informing the design of future quantum technologies.

Quantum Chaos in Ising Spin Chains

Scientists investigate signatures of quantum chaos within Ising spin chains, systems incorporating both local and non-local couplings. While local Ising models can be either integrable or chaotic depending on interaction strengths, systems with non-local interactions generally exhibit a stronger tendency towards chaos, even with weak coupling. By examining the distribution of energy level spacings, researchers delineate the transition from integrable to chaotic regimes and characterise the degree of quantum chaos. This work contributes to a deeper understanding of quantum chaos in many-body systems and provides insights into the interplay between integrability, chaos, and non-local interactions in condensed matter physics.

Quantum Chaos, Krylov Complexity, and Thermalization

Research focuses on understanding quantum chaos, many-body dynamics, and operator growth, particularly through the lens of Krylov complexity. Foundational papers establish the link between classical chaos and quantum energy level statistics, and connect quantum chaos with eigenstate thermalization, explaining how isolated quantum systems can behave thermally. Studies explore how information spreads within quantum systems, crucial for understanding thermalization and chaos, and investigate operator complexity beyond the scrambling time. Krylov complexity, a method for quantifying the complexity of quantum states and circuits, is increasingly used to study scrambling and thermalization.

Recent work applies Krylov complexity to various systems to understand their dynamics and phase transitions, and explores its connection to integrability, chaos, and localization. Researchers also investigate Krylov complexity in the context of quantum field theory, often focusing on saddle-point approximations. This active area of research aims to develop tools to understand the fundamental principles of quantum chaos, thermalization, and information processing in complex quantum systems, with a growing interest in applying these concepts to realistic physical scenarios.

Non-Local Interactions Drive Quantum Chaos Emergence

Scientists have demonstrated a clear link between non-local interactions and the emergence of quantum chaos in Ising spin chains, achieving detailed characterization of the transition from predictable, integrable behavior to complex, chaotic dynamics. The work centers on examining energy level spacing ratios and Krylov complexity to probe these systems. Experiments reveal that introducing even weak non-local couplings significantly accelerates the onset of chaos compared to purely local interactions. Measurements of energy level spacing ratios show that for non-local Ising models with sufficient interaction strength, the average level spacing ratio deviates from values expected for integrable systems and approaches values characteristic of chaotic systems. These spectral features correlate with dynamical behavior, as evidenced by analysis of Krylov complexity, which exhibits rapid initial growth and saturation in chaotic regimes, contrasting with slower growth in integrable phases. This breakthrough delivers a quantitative means to distinguish between these phases, with the growth rate and saturation level of Krylov complexity serving as effective indicators, and underscores the crucial role of non-locality in amplifying chaos within quantum spin chains.

Long-Range Interactions Drive Quantum Chaos

This research investigates the emergence of chaotic behaviour in quantum spin chains, models frequently used to understand more complex materials. Scientists demonstrate that introducing long-range interactions between the spins significantly increases the tendency towards chaos, even when these interactions are weak, compared to systems with only nearest-neighbor connections. The team characterized this transition by examining the spacing between energy levels, revealing distinct patterns that indicate the onset of chaotic dynamics. The study introduces Krylov complexity as a tool to quantify and distinguish between integrable and chaotic systems, observing a characteristic rise and subsequent plateau in Krylov complexity over time in chaotic systems. The findings highlight how long-range interactions not only accelerate the development of chaos but also alter the complexity of the system’s dynamics, offering new insights into the fundamental properties of quantum many-body systems. Future work could explore the impact of disorder and different types of long-range interactions on the observed chaotic behaviour and complexity.