Researchers Build Long-Range Spin Chains with Predictable Correlation Spread

A thorough investigation into many-body Floquet models reveals a new understanding of dual-unitary dynamics in systems extending beyond nearest-neighbour interactions. Vladimir Al. Osipov and colleagues at Harbin Institute of Technology, in collaboration with Holon Institute of Technology and China Suzhou Research Institute and Duisburg-Essen University, have constructed a broad family of dual-unitary kicked spin chains featuring long-range interactions. The research shows that local two-point correlations propagate predictably along light-cone edges, offering an analytical approach applicable to operators with local support and sharply broadening the scope of these models.

Long-range interactions and light-cone propagation in dual-unitary spin chains

Dual-unitary kicked spin chains now extend beyond nearest-neighbour interactions, achieving a previously unattainable capability to model long-range interactions. Previously, models were restricted to interactions between adjacent spins, but functionality now extends to interaction ranges denoted as ‘r’, allowing connections between spins separated by any number of intervening sites. This represents a significant advancement, as many physical systems exhibit long-range interactions arising from phenomena such as dipole-dipole coupling, van der Waals forces, or interactions mediated by bosonic modes. A family of these models was constructed using pairs of Hadamard matrices, mathematical tools that enable these extended interactions while maintaining the predictable ‘dual-unitary’ property. Hadamard matrices are square matrices with entries of +1 or -1, possessing orthogonal rows and columns; their specific construction dictates the nature and range of the interactions within the spin chain.

Local two-point correlations within these chains propagate along ‘light-cone edges’, boundaries defined where distance equals the product of interaction range and time. These correlations arise between operators positioned at sites separated by ‘k’ lattice spaces, with ‘k’ equal to the product of the interaction range ‘r’ and time ‘t’. This propagation is analogous to the propagation of light within a light cone in special relativity, hence the terminology. The speed of propagation is determined by the interaction range ‘r’, meaning information cannot travel faster than this limit. Even with these long-range interactions, the models remain ‘dual-unitary’, a property vital for maintaining predictable dynamics, as verified using a kicked Ising spin chain with next-to-next-neighbour interactions. The dual-unitary property implies that the time evolution operator and its adjoint are both unitary, ensuring that the system’s dynamics are reversible and well-defined. This is crucial for reliable simulations and potential applications in quantum information processing. Current findings describe behaviour within idealised systems, and further work is needed to explore potential applications in quantum technologies and materials simulation. Specifically, understanding how these models behave in the presence of disorder or external driving forces is an important area for future research.

Demonstrating predictable quantum dynamics with limited interaction ranges

An increasing focus lies on understanding how complex quantum systems evolve, with models seeking to move beyond simplified assumptions. Successfully built was a new family of ‘dual-unitary’ systems, exhibiting predictable and reversible behaviour, specifically utilising next-to-next-neighbour interactions. The significance of this lies in the fact that many-body quantum systems are notoriously difficult to simulate due to the exponential growth of the Hilbert space with system size. Dual-unitary systems offer a pathway to circumvent this difficulty by providing a framework for analytical calculations and efficient numerical simulations. While demonstrating the principle, the approach doesn’t yet definitively scale to all possible long-range interactions or larger, more complex systems, and future work will focus on addressing these limitations. Scaling to larger systems requires careful consideration of computational resources and the development of more efficient algorithms.

The team, a collaboration between Harbin Institute of Technology, Holon Institute of Technology, China Suzhou Research Institute and Duisburg-Essen University, broadened the scope of dual-unitary systems previously constrained by interactions limited to immediately adjacent components. Prior research on dual-unitary systems, such as the kicked Ising chain (KIC), has provided valuable insights into quantum chaos and many-body localisation, but these models were limited by their short-range interactions. By constructing a family of kicked spin chains utilising Hadamard matrices, they achieved long-range interactions, where components can connect irrespective of the distance separating them. This offers a tractable platform for exploring long-range interactions, previously limited by simpler systems like the kicked Ising spin chain, and allows for investigation of more complex quantum phenomena. The use of Hadamard matrices provides a systematic way to generate a diverse range of long-range interactions, enabling researchers to explore the effects of different interaction topologies on the system’s dynamics. This research opens avenues for investigating the emergence of collective behaviour and entanglement in quantum systems with long-range connectivity, potentially leading to new insights into the behaviour of complex materials and the development of novel quantum technologies. The ability to analytically track the propagation of correlations, as demonstrated by the light-cone behaviour, is a particularly valuable feature of these models, as it allows for a deeper understanding of how information spreads within the system.

Researchers successfully created a family of dual-unitary kicked spin chains featuring long-range interactions, extending beyond the nearest-neighbor limitations of previous models like the kicked Ising chain. This is significant because it provides a new, analytically tractable system for studying how quantum correlations propagate, specifically demonstrating propagation along edges defined by the interaction range. The team used Hadamard matrices to achieve these long-range connections and are now focusing on scaling this approach to larger, more complex systems. This work enhances understanding of complex quantum phenomena and collective behaviour in connected quantum systems.