Researchers Discover ‘Quadratic Chaos’ in Two-Body Hamiltonians, Revealing Sachdev-Ye-Kitaev Model Parallels

The behaviour of complex quantum systems remains a fundamental challenge in physics, and researchers are now exploring how minimal models can shed light on this area. Pallab Basu, Suman Das, and Pratik Nandy, from institutions including the University of the Witwatersrand and Kyoto University, investigate a new form of quantum chaos arising from simple two-body interactions. Their work reveals that these systems, unlike their more orderly counterparts, exhibit chaotic dynamics mirroring those found in complex models like the Sachdev-Ye-Kitaev (SYK) model, but with a crucial difference, they are based on bosons rather than fermions. This research is significant because it demonstrates a pathway towards understanding information scrambling and quantum chaos using resource-efficient models, potentially paving the way for experiments on emerging quantum technologies and offering insights into the behaviour of black holes.

SYK Model, Quantum Chaos and Complexity

A substantial body of research explores the Sachdev-Ye-Kitaev (SYK) model, quantum chaos, and related concepts like operator growth, Krylov complexity, free probability, and entanglement measures. This work aims to understand the fundamental properties of complex quantum systems and how information behaves within them. The SYK model, a simplified model of interacting fermions, serves as a crucial testbed for studying quantum gravity and quantum chaos due to its unique solvability and connection to black hole physics. Researchers are particularly interested in how operators evolve over time, a process quantified by Krylov complexity, and how this relates to the scrambling of information in chaotic systems.

Free probability provides tools for analyzing the statistical properties of these quantum systems, while entanglement measures reveal how quantum correlations grow and spread. Studies also investigate open quantum systems, which interact with their environment, and how dissipation and decoherence affect chaotic dynamics. Recent trends demonstrate a growing interest in exploring the dynamics of open quantum systems, using Krylov complexity to characterize quantum phase transitions, and connecting quantum chaos to quantum information theory. This research represents a vibrant and active area at the intersection of quantum physics, many-body physics, and quantum information theory, with the SYK model serving as a central platform for exploring fundamental questions about quantum chaos, information scrambling, and the emergence of spacetime.

Quadratic Chaos Mirrors Complex Quantum Spectra

Researchers investigated minimal two-body Hamiltonians exhibiting chaotic behaviour, termed quadratic quantum chaos, and discovered striking parallels to the complex Sachdev-Ye-Kitaev (SYK) model. Unlike typical integrable systems, these hard-core boson models demonstrate genuinely chaotic dynamics, opening new avenues for understanding complex quantum systems. The team’s analysis centers on how the energy levels, or spectra, of these models behave, and how this behaviour signals the presence of chaos. Experiments revealed that the density of states for these models closely resembles a Gaussian distribution, a characteristic also observed in more complex Majorana fermion systems.

Further investigation into spectral statistics employed the analysis of level spacing ratios, a technique used to identify correlations between energy levels. Results demonstrate that these models exhibit level repulsion, a hallmark of quantum chaos where energy levels avoid being too close together, in contrast to the clustering seen in integrable systems. The team extended this analysis to higher-order spacing ratios, revealing long-range correlations within the spectrum and providing a more refined diagnostic of spectral rigidity. Researchers defined a family of global operators and demonstrated that these operators act as conserved charges, splitting the Hamiltonian’s spectrum into distinct parity sectors, highlighting the interplay between symmetry, conservation laws, and the emergence of chaotic behaviour. The simplicity and bosonic nature of these models make them potentially valuable for probing chaos and information scrambling on near-term quantum devices, potentially offering a resource-efficient approach to exploring fundamental questions in quantum physics.

Random Eigenstates Signal Quantum Chaos Emergence

This research investigates a simplified model exhibiting quantum chaos, termed ‘quadratic chaos’, built from minimal two-body interactions. The team demonstrates that these models, unlike their integrable counterparts, display chaotic dynamics closely resembling the more complex Sachdev-Ye-Kitaev (SYK) model. This chaotic behaviour is confirmed through analysis of the energy spectrum and measures of operator growth, revealing characteristics consistent with the scrambling of quantum information. Specifically, the study shows that the models exhibit level repulsion in their energy spectra and demonstrate the emergence of ‘freeness’ in their dynamics, a key indicator of chaotic systems. Furthermore, the analysis of individual energy eigenstates reveals that they converge towards randomness as the system size increases, though constrained by the local nature of the interactions, indicating a ‘weakly chaotic’ character. The simplicity and bosonic nature of these models make them potentially valuable for probing quantum chaos and information scrambling using near-term quantum devices.