Spread of Entanglement in Generalized Kicked Ising Chain

This paper investigates the dynamics of entanglement in generalized kicked Ising chains, extending the standard qubit model (local dimension q=2) to higher-dimensional qudits (q > 2). The study focuses on identifying "dual-unitary" points—special parameter settings where the system exhibits space-time duality, enabling exact analytical treatment of quantum information spread.

A central contribution of this work is the classification of dual-unitary points across different local dimensions. While such points are well-known for q=2, the authors prove that they exist analytically only for q=3 and q=4. For q >= 5, the authors demonstrate that the requirements for dual-unitarity—specifically that all transition amplitudes of the kick operator have identical magnitude—cannot be satisfied by any single kicking strength. This breakdown is attributed to the over-constrained nature of the interference conditions in larger Hilbert spaces, which the authors confirm using an asymptotic analysis involving Bessel functions.

For the q=3 case (the kicked Potts model), the authors utilize a transfer-matrix approach combined with a replica trick to compute the exact growth of Rényi and von Neumann entanglement entropies. Starting from a specific class of solvable initial states, they show that the entanglement entropy grows ballistically (linearly with time) until it reaches a saturation value determined by the subsystem size. This provides a rigorous benchmark for understanding how quantum information propagates in higher-dimensional quantum systems.

These findings are particularly relevant to the design of quantum computing architectures. By identifying the constraints on dual-unitarity, the paper clarifies the limits of exact solvability in many-body systems. Furthermore, the results for the q=3 Potts model are significant because these systems can be described using parafermions, which are linked to topological quantum computing and non-trivial anyonic statistics.