Hybrid Brownian SYK-Hubbard Model Exhibits Spectral Transitions, Signaling Mottness and Quantum Chaos

The behaviour of strongly interacting systems presents a long-standing challenge in physics, and researchers continually seek simplified models to capture their essential characteristics. Ning Sun, Peng Zhang, and Pengfei Zhang, from Fudan University and Renmin University of China, now introduce a novel approach, the Brownian SYK-Hubbard model, which combines the random interactions of the Sachdev-Ye-Kitaev model with more conventional on-site interactions. This hybrid model allows scientists to investigate how these local and non-local effects combine, revealing a transition to a Mott insulating state as interactions strengthen and demonstrating complex changes in the system’s spectral properties over time. Crucially, the team’s calculations also reveal a breakdown of expected limits on chaotic behaviour, establishing a new, analytically solvable framework for understanding the interplay between chaos and strong interactions in complex systems.

Brownian SYK Model and Quantum Chaos

This research presents a comprehensive investigation into quantum chaos, many-body physics, and its connections to concepts like black holes and quantum information. Scientists explore how classical chaos manifests in quantum systems by studying the out-of-time-ordered correlator, a key indicator of chaotic behaviour and the ‘butterfly effect’. The study utilizes the Sachdev-Ye-Kitaev (SYK) model, a solvable model of interacting particles that exhibits properties similar to black holes, extending it to include noise through the Brownian SYK model. The work delves into the behaviour of systems with many interacting particles, particularly fermions, and draws parallels between these systems and the physics of black holes, including the information paradox and the emergence of spacetime.

Researchers also investigate how quantum information is processed and scrambled in these chaotic systems, relating to concepts like entanglement. This research aims to understand the fundamental principles governing quantum chaos and its implications for quantum information processing and the emergence of spacetime. This is a highly theoretical study, deeply rooted in condensed matter physics, quantum field theory, and quantum information theory, drawing on a vast body of existing literature. This research represents a culmination of ongoing work, building on many recent developments in the field, and offers a state-of-the-art exploration of the frontiers of quantum chaos and its connections to other fundamental areas of physics.

Brownian SYK-Hubbard Model and Observables Calculation

Scientists engineered the Brownian SYK-Hubbard model, a novel system combining the all-to-all random interactions of the Sachdev-Ye-Kitaev (SYK) model with on-site Hubbard interactions, to investigate how random dynamics and local correlation effects interact. The system consists of numerous sites, each hosting four distinct Majorana fermion modes, and researchers imposed rules governing their behaviour to define their fermionic properties. The team analytically determined physical observables using a limited number of replicas and Keldysh contours, enabling the computation of the two-point function and single-particle spectrum. Analysis of the single-particle spectrum revealed a transition from a single peak to a two-peak structure as interaction strength increased, signalling the onset of Mottness, a characteristic feature of correlated electron systems.

Further investigation of the spectral form factor revealed a sequence of dynamical transitions at longer evolution times induced by strong Hubbard interactions. To analyze two-replica observables, the study pioneered a method for computing the out-of-time-order correlator, identifying a family of generalized ladder diagrams that fully capture the effects of the Hubbard interaction. This approach explicitly demonstrates a violation of the conventional bound on branching time, characteristic of SYK-like systems, and opens new avenues for exploring sub-AdS holography. The team’s work establishes a new analytically tractable platform for exploring the effects of Hubbard interactions in chaotic many-body systems, providing insights into the behaviour of strongly correlated materials.

Mott Transition in Brownian SYK-Hubbard Model

This work presents a novel theoretical platform, the Brownian SYK-Hubbard model, designed to explore the interplay between random interactions and local correlation effects in strongly interacting systems. Researchers successfully combined the all-to-all random interactions of the Sachdev-Ye-Kitaev (SYK) model with on-site Hubbard-type interactions, creating a hybrid model amenable to analytical treatment. Investigations into the single-particle spectrum revealed a significant transition; as interaction strength increases, the spectrum shifts from a single peak to a distinct two-peak structure, definitively signalling the onset of Mottness, a hallmark of correlated electron systems. Further analysis focused on the spectral form factor, demonstrating a sequence of dynamical transitions as the evolution time increases, ultimately reaching a plateau in the long-time limit under strong Hubbard interactions.

This behaviour indicates a complex interplay between the random and local interactions influencing the system’s dynamics. For two-replica observables, scientists computed the out-of-time-order correlator using a series of modified ladder diagrams, allowing them to determine the quantum Lyapunov exponent. Crucially, measurements reveal a violation of the established bound on branching time, a characteristic limitation of conventional SYK-like systems. This breakthrough demonstrates the potential for exploring new regimes of chaotic many-body physics beyond the constraints of previous models. The results establish a new analytically tractable platform for investigating the effects of Hubbard interactions in chaotic systems, opening avenues for understanding complex phenomena in materials science and fundamental physics.

Hubbard Interactions Drive Spectral and Dynamical Transitions

This research introduces the Brownian SYK-Hubbard model, a new theoretical framework for investigating the complex interplay between strong interactions and chaotic behaviour in many-body systems. By combining the all-to-all connectivity of the Sachdev-Ye-Kitaev model with on-site Hubbard interactions, scientists have created a solvable model that reveals how local correlation effects influence chaotic dynamics. Results demonstrate a transition in the single-particle spectrum, moving from a single peak to a two-peak structure as interaction strength increases, signalling the emergence of Mott-like behaviour. Further analysis of the spectral form factor reveals a series of dynamical transitions with increasing evolution time, ultimately reaching a stable state under strong Hubbard interactions.

Importantly, calculations of the out-of-time-order correlator demonstrate a violation of established bounds on branching time, indicating that this model represents a distinct class of systems beyond traditional SYK-like models. This achievement establishes a new, analytically tractable platform for exploring the effects of Hubbard interactions in chaotic systems, offering insights into phenomena not captured by existing theoretical tools. Future research directions include exploring entanglement dynamics and extending this modelling approach to systems relevant to superconductivity and magnetism. This work represents a significant step towards understanding the fundamental properties of strongly interacting systems and opens new avenues for theoretical investigation.