Tuning Quantum Chaos: A New Model Bridges Theory and Experiment

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Author: Denis Avetisyan

Researchers unveil a tunable model that explores the transition between different chaotic regimes in quantum many-body systems.

Through a tunable interaction between spinless fermions and bosonic modes—realized via optical cavities and engineered disorder—a system transitions from single-particle chaotic behavior at low boson mass to fully many-body chaotic dynamics at high mass, exhibiting a crossover regime where both behaviors coexist and evidenced by the spectral form factor.
Through a tunable interaction between spinless fermions and bosonic modes—realized via optical cavities and engineered disorder—a system transitions from single-particle chaotic behavior at low boson mass to fully many-body chaotic dynamics at high mass, exhibiting a crossover regime where both behaviors coexist and evidenced by the spectral form factor.

This paper introduces the Yukawa-SYK model, a theoretically solvable framework for studying the emergence of complex holographic phases and its potential realization in ultracold atom experiments using cavity QED.

Understanding the transition from simple to complex quantum behavior remains a central challenge in physics. This is addressed in ‘From single-particle to many-body chaos in Yukawa–SYK: theory and a cavity-QED proposal’, which introduces the Yukawa-SYK (YSYK) model as a tunable platform bridging single-particle and many-body chaotic regimes. By characterizing finite-size effects and spectral properties, we demonstrate that the YSYK model interpolates between the SYK$_2$ and SYK$_4$ limits, revealing distinct dynamical phases with partial ergodicity breaking and prethermalization. Could this model offer a pathway towards experimentally realizing and observing complex holographic phases in ultracold atomic systems?

Beyond the SYK Model: Mapping Complex Quantum Dynamics

The Sachdev-Ye-Kitaev (SYK) model, a cornerstone in quantum chaos research, offers a tractable framework for exploring black hole-like behavior in condensed matter systems. However, its inherent simplicity limits the study of transitions between chaotic phases and realistic physical scenarios. The YSYK model extends this framework by incorporating bosonic fields, augmenting the fermionic Hamiltonian and enabling the investigation of boson-fermion interactions. This expansion allows for the observation of distinct chaotic regimes and phase transitions inaccessible within the standard SYK model.

Disorder-averaged out-of-time-ordered correlations (OTOCs) of the YSYK model, calculated for a small boson mass and eight fermions with four bosonic modes, reveal a two-step scrambling process characterized by an initial prethermal plateau coinciding with the saturation value of the complex SYK2 model before fully scrambling, while larger boson masses indicate a deviation from the SYK2 regime.
Disorder-averaged out-of-time-ordered correlations (OTOCs) of the YSYK model, calculated for a small boson mass and eight fermions with four bosonic modes, reveal a two-step scrambling process characterized by an initial prethermal plateau coinciding with the saturation value of the complex SYK2 model before fully scrambling, while larger boson masses indicate a deviation from the SYK2 regime.

This extension bridges the gap between theoretical models and experimental observations in areas like high-temperature superconductivity and quantum gravity, offering a pathway to understanding emergent phenomena in strongly correlated systems. Every image is a challenge to understanding, not just a model input.

Tuning the Quantum Landscape: The ω0/g2/3 Ratio

The Yukawa-SYK (YSYK) model allows exploration of the interplay between fermionic and bosonic degrees of freedom. Within this model, the ratio ω0/g2/3 functions as a critical control parameter, governing the system’s behavior and enabling interpolation between SYK2-like and SYK4-like chaotic regimes. These regimes exhibit unique spectral signatures, necessitating distinct analytical approaches for accurate modeling.

Early-time disorder-averaged out-of-time-ordered correlations (OTOCs) for the YSYK model, calculated with eight fermions, four bosonic modes, and a boson mass of ten, demonstrate the effectiveness of a numerical filter in isolating oscillations from the decaying component of the correlation function.
Early-time disorder-averaged out-of-time-ordered correlations (OTOCs) for the YSYK model, calculated with eight fermions, four bosonic modes, and a boson mass of ten, demonstrate the effectiveness of a numerical filter in isolating oscillations from the decaying component of the correlation function.

The transition between these regimes, controlled by ω0/g2/3, represents a qualitative shift in the system’s response and correlation functions.

Decoding Chaos: Spectral Signatures and the Path to Order

A comprehensive analysis of the YSYK model’s chaotic behavior is conducted through Density of States (DOS), Spectral Form Factor (SFF), and Gap Ratio Distribution. These tools characterize the model’s quantum properties and identify key signatures of its chaotic dynamics.

Examination of the gap ratio distribution reveals a transition as the parameter ω0/g2/3 is varied. Initially, the distribution exhibits Poisson statistics; however, as ω0/g2/3 increases, it transitions to a Gaussian Unitary Ensemble (GUE)-like plateau, indicating strong quantum chaos. Concurrently, the Spectral Form Factor (SFF) shifts from a linear dependence (SYK2) to a plateau (SYK4).

The spectral form factor K(t) for the normal-ordered effective model, calculated at half filling with eight fermions, exhibits increasing proximity to the SYK4 benchmark as the rank of the antisymmetric couplings increases, as demonstrated by data averaged over 500 realizations and normalized by D2.
The spectral form factor K(t) for the normal-ordered effective model, calculated at half filling with eight fermions, exhibits increasing proximity to the SYK4 benchmark as the rank of the antisymmetric couplings increases, as demonstrated by data averaged over 500 realizations and normalized by D2.

These transitions and spectral characteristics validate the YSYK model as a robust framework for capturing complex quantum phenomena and demonstrating emergent chaotic behavior.

Experimental Realizations: Ultracold Atoms and the Quest for Quantum Control

Ultracold atoms confined within optical cavities represent a promising platform for experimentally realizing the Yukawa-SYK (YSYK) model. These cavities allow precise control over atomic interactions and provide the necessary conditions to observe emergent phenomena predicted by the model.

The optical cavities facilitate the creation of the Yukawa interaction between fermions and bosons, crucial for the YSYK model’s dynamics and resulting non-Fermi liquid behavior. By tuning the cavity parameters, researchers can control the strength and range of this interaction, effectively ‘dialing in’ the desired Hamiltonian.

This experimental setup offers a unique opportunity to test theoretical predictions regarding the YSYK model, including its spectral properties and entanglement structure. It also opens avenues for exploring potential applications in quantum simulation and materials discovery, potentially leading to the design of novel quantum materials with exotic properties. The interplay between controlled parameters and observed outcomes is a glimpse into the hidden architecture of complex systems.

The exploration of the Yukawa-SYK model, as detailed in the study, reveals a fascinating interplay between order and disorder, mirroring the transition between different chaotic regimes. This pursuit of understanding complex systems through solvable models aligns with the sentiment expressed by Max Planck: “When you change the way you look at things, the things you look at change.” The YSYK model provides a novel lens through which to examine holographic phases, demonstrating that a shift in theoretical approach—in this case, by exploring a tunable chaotic system—can indeed reveal previously obscured properties of quantum complexity. The model’s capacity to bridge SYK2 and SYK4 behaviors highlights the importance of adopting innovative perspectives to decipher the intricate patterns governing quantum phenomena.

What’s Next?

The introduction of the Yukawa-SYK model serves not as a destination, but as a refined vantage point. The observed tunability between chaotic regimes – a seemingly simple adjustment of a parameter – belies the underlying complexity of many-body quantum systems. The model’s solvability is, of course, a temporary reprieve from the usual intractability, and future work must address the inevitable distortions introduced by realistic physical systems. A critical examination of finite-size effects, beyond those already considered, will be crucial. The precise mechanisms by which ergodicity breaking manifests – or fails to manifest – in more complex variations deserve careful attention.

The proposal for cavity-QED realization, while promising, implicitly acknowledges the challenge of mapping theoretical elegance onto experimental reality. Ultracold atoms, despite their controllability, present their own set of constraints. The crucial question remains: can these systems truly capture the holographic phases suggested by the theory, or will the necessary experimental precision prove insurmountable? The spectral form factor, a useful diagnostic, is merely one slice of a much larger, and likely far more nuanced, dataset.

Ultimately, the value of the YSYK model may lie not in its perfect replication of any particular physical system, but in its capacity to illuminate the fundamental patterns governing quantum chaos. The exploration of alternative coupling schemes, beyond the Yukawa potential, could reveal entirely new chaotic regimes. It is a reminder that even in the pursuit of simplified models, the universe retains a remarkable capacity for surprise.

Original article: https://arxiv.org/pdf/2511.04762.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-10 14:45