A family of finite range kicked Ising models preserves dual unitarity across inter sublattice couplings, yielding exact n Rényi entropies at r=2 and a natural extension to larger ranges and heterogeneous local dimensions.
A new construction of finite-range kicked Ising models shows that the closed-form entanglement dynamics long associated with dual-unitary circuits are not strictly a nearest-neighbor phenomenon. The paper, posted to arXiv, builds a staggered family in which dual-unitarity holds on each of two coupled sublattices and survives the inter-sublattice couplings, yielding an exact expression for all n-Rényi entanglement entropies at the minimal interaction range r=2 (Exact Entanglement Dynamics Beyond Nearest-Neighbor Dual-Unitary Floquet Systems).
Dual-unitarity has, until now, been a property largely demonstrated in strictly nearest-neighbor Floquet circuits. In those systems, the circuit is unitary in time and unitary under a swap of space and time, and that double-unitarity is what makes the entanglement entropy between two halves of the system solvable in closed form. Going beyond nearest-neighbor interactions has generally broken this structure. The swap-symmetry of the time-evolution operator stops holding once a gate can act on a wider spatial region, and the analytic results fall away with it.
The new construction sidesteps that obstruction by splitting the lattice. Each sublattice is, on its own, an ordinary dual-unitary kicked Ising chain. The two sublattices are then coupled, but the coupling is arranged so that the composite evolution remains dual-unitary. The authors show that the inter-sublattice couplings do not obstruct the property, and the resulting model is therefore still analytically tractable in the same sense as the nearest-neighbor case.
The concrete result sits at r=2, the smallest interaction range beyond nearest neighbor. For this case, the authors derive closed-form expressions for all n-Rényi entropies at all times. The structure is clean. The entropy of the full system is the sum of the two coupled sublattice contributions, an additive decomposition that makes the result reusable. The per-sublattice entropies are the same objects one would compute in two independent nearest-neighbor dual-unitary chains, and the coupling does not introduce new correlation terms in the entropy.
The framework is not confined to r=2. The authors note that the construction extends naturally to larger finite interaction ranges, and to systems with heterogeneous local Hilbert spaces, without requiring additional assumptions. Each step preserves the staggered structure, so the additive decomposition carries through as the range grows. Heterogeneous local dimensions, where the two sublattices carry different spin or qudit sizes, fit the same scheme.
Two caveats sharpen what the result is and is not. First, the paper is a preprint; the construction and the r=2 closed form have not yet been peer-reviewed, and the author list and affiliations are not present in the abstract record and should be checked against the arXiv listing or the PDF before being used in a byline. Second, the construction is a family of models, not a classification theorem. It shows that dual-unitarity can be preserved at finite range, but it does not exhaustively characterize which finite-range models share the property. Entanglement growth in generic finite-range Floquet circuits, and in experimental systems, is not addressed.
What the paper does offer, and what makes it worth attention, is a controlled analytical setting for studying exact entanglement growth beyond strictly nearest-neighbor models. The staggered decomposition gives a working tool. A reader with a result in a nearest-neighbor dual-unitary chain can now ask how it changes when the two sublattices are coupled, with the entropy still in closed form. The structural contribution is exact solvability surviving the move beyond nearest neighbors, on a family of models built to keep it.