Shaking the Hubbard Model Creates Sachdev-Ye-Kitaev Physics and Enables Cold-Atom Realization

The pursuit of understanding complex quantum systems has led physicists to the Sachdev-Ye-Kitaev (SYK) model, a theoretical framework with implications for fields ranging from high-temperature superconductivity to the study of black holes and chaotic behaviour. However, experimentally realising the SYK model presents a significant challenge. Charles Creffield, Fernando Sols, Marco Schirò, and Nathan Goldman demonstrate a pathway to overcome this obstacle, revealing how a technique called ‘kinetic driving’ effectively reshapes interactions within Hubbard-type models. Their work shows that this method suppresses individual particle movements and generates the all-to-all connectivity characteristic of the SYK model, verified through detailed comparisons of key quantum properties. This achievement suggests that manipulating cold atoms offers a viable and precise means of simulating this elusive quantum system, potentially unlocking new insights into its fundamental properties.

Simulating Quantum Chaos with Driven Hubbard Models

Scientists engineered a novel method for simulating complex physical systems using cold atoms trapped in optical lattices. The work addresses the significant challenge of experimentally realizing the Sachdev-Ye-Kitaev (SYK) model, a theoretical construct relevant to areas like high-temperature superconductivity and black hole physics. The team pioneered a technique called “kinetic driving”, a specific form of Floquet engineering, to effectively eliminate single-particle processes and create all-to-all interactions crucial for mimicking SYK behavior. This approach involves periodically modulating the hopping amplitude of bosons on a one-dimensional lattice.

The study began with the Bose-Hubbard model, describing bosons moving on a lattice with hopping amplitude and onsite repulsion. Researchers then applied kinetic driving, varying the hopping amplitude with time, ensuring the time-average is zero. Utilizing theoretical techniques, the team derived an effective Hamiltonian for the kinetically-driven Bose-Hubbard (KDBH) model. This effective Hamiltonian consists of quartic interaction terms between bosons, eliminating the original single-particle hopping processes and closely resembling the SYK model, characterized by all-to-all interactions between particles.

To validate the connection to the SYK model, scientists compared the KDBH Hamiltonian with the bosonic SYK model, which features random interactions. The team demonstrated that the KDBH Hamiltonian possesses the same structure of interaction terms as the SYK model, automatically satisfying the required bosonic exchange statistics and Hermiticity. While the interaction amplitudes in the KDBH model depend on the driving parameters, analysis revealed a sparse Hamiltonian, yet retaining sufficient connectivity to emulate SYK physics. The distribution of amplitudes differs from the dense distribution of the SYK model, but the study demonstrates this does not prevent the KDBH model from accurately reproducing SYK behavior.

To quantify this fidelity, scientists investigated the chaoticity of the KDBH model, utilizing probes commonly employed in studies of quantum chaos. They found that the model mirrored the behavior of the bosonic SYK model. Further analysis focused on the spectral form factor, a measure of quantum chaos, and results demonstrate a universal structure, confirming the presence of the expected chaotic behavior. Scaling the spectral form factor collapsed curves onto each other, displaying the required universal structure. Measurements of the ramp time revealed a precise inverse relationship with the system size.

To further validate the connection to SYK physics, scientists calculated the out-of-time ordered correlation function, a measure of quantum scrambling and information delocalization. Results show that the decay of this function reveals a finite “butterfly velocity”, indicating the propagation of information through the system. In contrast to the Bose-Hubbard model, the kinetic driving approach creates a system where information scrambles rapidly, mirroring the behavior predicted by the SYK model. These findings establish a new pathway for simulating complex quantum systems and exploring fundamental questions in theoretical physics.

This work establishes that cold-atom systems offer a practical and precise platform for simulating the SYK model, previously a significant experimental challenge. Researchers have demonstrated a method for simulating the Sachdev-Ye-Kitaev (SYK) model, a theoretical framework with implications for understanding high temperature superconductivity, black holes, and chaotic systems. The team achieved this by employing kinetic driving on a Hubbard model, generating the all-to-all interactions characteristic of the SYK model. By comparing key properties, such as the spectral form factor and out-of-time ordered correlations, the researchers verified that the driven system accurately reproduces the physics predicted by the SYK model.