Chaos Parameter Shift Reveals Hidden Order in Quantum Systems

Scientists Jia-jin Feng and Quntao Zhuang at University of Southern California investigated the spectral structure of reset-driven Floquet quantum channels, revealing a pathway from order to chaos. Their findings show how tuning a chaos-controlling parameter induces a spectral transition linked to exceptional points, moving from a symmetry-constrained ergodic regime to a fully chaotic one. The study establishes a clear connection between the channel spectrum and experimentally accessible probes of quantum mutual information, potentially offering new ways to characterise and understand complex dynamical regimes such as chaotic, ergodic, many-body localised, and scarred behaviours.

Spectral transitions reveal dynamical regimes in Floquet quantum channels

Leading channel eigenvalues shifted from a symmetry-constrained ergodic regime to a fully chaotic one, evidenced by a dramatic increase in complex-conjugate eigenvalue pairs. Previously, discerning these regimes required intricate analysis of system behaviour, often involving time-consuming simulations of the underlying many-body dynamics. This spectral transition, induced by exceptional points where eigenvalues coalesce and split, provides a new method to characterise quantum dynamics, bypassing complex calculations of overall system behaviour. Exceptional points represent singularities in the parameter space of the Hamiltonian, where two or more eigenvalues become degenerate and the corresponding eigenvectors merge. Their presence signals a breakdown of the standard perturbative approach to quantum mechanics and can lead to enhanced sensitivity to external perturbations. Tuning a chaos-controlling parameter within reset-driven Floquet quantum channels revealed a clear link between spectral organization and experimentally accessible quantum mutual information, a connection that had previously remained elusive. Quantum mutual information quantifies the correlation between two quantum systems and serves as a sensitive probe of many-body entanglement and information transfer. The ability to relate channel spectra to this measurable quantity provides a crucial bridge between theoretical models and experimental observations. Further validation of these findings came from examining systems with varying degrees of anisotropy. Deviations from equal coupling coefficients in the Heisenberg model resulted in a corresponding increase in exceptional points and complex eigenvalues. The Heisenberg model, a cornerstone of quantum magnetism, describes the interactions between spins in a solid and is frequently used to model many-body systems. Introducing anisotropy, by altering the coupling strengths along different spatial directions, disrupts the symmetry of the Hamiltonian and promotes the emergence of chaotic behaviour.

Tracking energy flow in open quantum systems via reset-driven Floquet channels

Categorising the behaviours of isolated quantum systems is becoming increasingly achievable, yet understanding how these systems respond when connected to an external environment remains a formidable challenge. This work offers a new spectral approach to tracking energy flow within these ‘open’ systems, revealing distinct spectral signatures for chaotic and localised regimes, and crucially connecting channel eigenvalues to measurable relaxation dynamics. Open quantum systems are ubiquitous in nature, representing realistic physical scenarios where interactions with the environment inevitably lead to decoherence and dissipation. Reset-driven Floquet quantum channels provide a powerful framework for studying the dynamics of such systems by effectively mimicking the repeated interactions between the system and a bath. Information flow through repeated applications of the quantum channel was clearly tracked via decomposition of initial states within the eigenoperator basis. This provides a pathway to observe the effects of spectral transitions. The eigenoperator basis, constructed from the eigenvectors of the quantum channel, offers a natural coordinate system for analysing the evolution of quantum states and identifying the dominant modes of information transfer. By projecting initial states onto this basis, researchers can effectively decompose the system’s dynamics into a superposition of independent channels, each characterised by a specific eigenvalue.

The abstract references a “circular law” governing eigenvalue distribution without quantifying its radius in the chaotic regime, indicating a potential avenue for future research. The circular law, a well-established result in random matrix theory, predicts that the eigenvalues of large random matrices tend to distribute uniformly within a circle in the complex plane. Observing deviations from this law, or accurately determining the radius of the circle, can provide insights into the underlying structure of the quantum channel and the degree of chaos present in the system. Reset-driven Floquet quantum channels now offer a method for distinguishing between different types of quantum behaviour. These channels, created by repeatedly applying quantum operations and ‘resetting’ the system, reveal unique spectral signatures for each dynamical regime; a spectrum functions as a fingerprint of the channel’s behaviour. The ‘reset’ operation effectively removes any memory of the system’s past, ensuring that the dynamics remain confined to the Floquet subspace and simplifying the analysis. While these results establish a strong connection between channel spectra and open many-body dynamics, a systematic correspondence between Hamiltonian properties and channel spectra remains to be fully explored for a wider range of models. Investigating different Hamiltonian structures, such as those exhibiting long-range interactions or disorder, could reveal new and unexpected spectral features. Analysis of the anisotropic Heisenberg model revealed that as the system moved further from symmetry, the number of complex eigenvalues grew, corroborating the link between spectral characteristics and underlying Hamiltonian properties. Complex eigenvalues indicate the presence of unstable modes in the quantum channel, leading to exponential decay of certain quantum states and contributing to the overall chaotic behaviour of the system. This finding highlights the importance of symmetry in controlling the dynamics of open quantum systems and provides a potential route for designing systems with tailored properties.

The research demonstrated that the spectrum of reset-driven Floquet quantum channels can differentiate between chaotic, ergodic, many-body localised, and scarred dynamical regimes. This is significant because the channel spectrum acts as a fingerprint, revealing information about a system’s behaviour without needing detailed knowledge of its internal workings. By tuning a chaos-controlling parameter, researchers observed a transition in the channel’s spectral structure, linked to the breaking of symmetry constraints. The authors suggest further work is needed to fully explore the relationship between Hamiltonian properties and these channel spectra across a wider range of models.