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arXiv:2606.13857

Local correlations in long-range dual-unitary kicked Hamiltonian chains

Vladimir Al. Osipov, Marc Cedric Spyra, Jana Carolina Schumann, Thomas Guhr, Boris Gutkin

quant-phcond-mat.dis-nnSubmitted Jun 11, 2026• Announced Jun 15, 2026• 0 citations
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Abstract

Many-body Floquet models with exact space--time symmetry, such as the kicked Ising spin chain (KIC), provide natural examples of systems with dual-unitary dynamics. The requirement of exact space--time symmetry is, however, highly restrictive, as it permits only nearest-neighbor interactions. Based on a pair of Hadamard matrices, we construct a wide family of dual-unitary kicked spin chains with long-range interactions. We show that local two-point correlations in such models propagate along the light-cone edges \( |n| = r|t| \), where \(r\) is the interaction range, and can be derived analytically for operators with local support. This approach is illustrated using the example of a kicked Ising spin chain with next-to-next-neighbor interactions.

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Many-body Floquet models with exact space--time symmetry, such as the kicked Ising spin chain (KIC), provide natural examples of systems with dual-unitary dynamics. The requirement of exact space--time symmetry is, however, highly restrictive, as it permits only nearest-neighbor interactions. Based on a pair of Hadamard matrices, we construct a wide family of dual-unitary kicked spin chains with long-range interactions. We show that local two-point correlations in such models propagate along the light-cone edges ( |n| = r|t| ), where (r) is the interaction range, and can be derived analytically for operators with local support. This approach is illustrated using the example of a kicked Ising spin chain with next-to-next-neighbor interactions.
We show that for dual-unitary kicked chains, built upon a pair of complex Hadamard matrices, correlators of strictly local, traceless operators vanish identically for sufficiently long chains. On the other hand, operators supported at pairs of adjacent chain sites, generically, exhibit nontrivial correlations along the light cone edges. In agreement with Bertini et. al. [Phys. Rev. Lett. 123, 210601 (2019)], they can be expressed through the expectation values of a transfer matrix TTT. Furthermore, we identify a remarkable family of dual-unitary models where an explicit information on the spectrum of TTT is available. For this class of models we provide a closed analytical formula for the corresponding two-point correlators. This result, in turn, allows an evaluation of local correlators in the vicinity of the dual-unitary regime which is exemplified on the kicked Ising spin chain.
Exact results using dual-unitarity largely rely on nearest-neighbor structures, while finite-range interactions typically lead to complications. Going beyond the usual nearest-neighbor setting, we introduce an analytically tractable family of finite-range kicked Ising models that admit exact closed-form entanglement dynamics. The construction is based on a staggered structure in which dual-unitarity is present on sublattices that are then coupled to each other. The central observation is that these inter-sublattice couplings do not obstruct the dual-unitarity of the resulting model. For the minimal interaction range of r=2r= 2r=2, we derive exact expressions for all the n−n-n−Rényi entanglement entropies at all times and show that the result is the sum of the two coupled sublattice contributions. Our framework extends naturally to larger finite interaction ranges and to systems with heterogeneous local Hilbert spaces, without additional assumptions. It thus provides a controlled setting for studying exact entanglement growth beyond strictly nearest-neighbor dual-unitary models.
We show that local correlators in a wide class of kicked chains can be calculated exactly at light-cone edges. Extending previous works on circuit lattice systems, the correlators between local operators are expressed through the expectation values of transfer matrices T\mathbf{T}T with small dimensions. For dual-unitary kicked chains, with spatial-temporal symmetry of the dynamics, this provides a full characterization of local correlators. Furthermore, we identify a remarkable family of dual-unitary models where an explicit information on the spectrum of T\mathbf{T}T is available. For this class of models we provide a closed analytical formula for the corresponding two-point correlators. The results are exemplified on the kicked Ising spin chain model.
ppp-Body ≃\simeq≃ Range p−1p-1p−1: Exact Order-Range Mapping and Dual-Unitarity
We introduce and study a periodically kicked version of a one-dimensional spin-1/21/21/2 Ising model with contiguous ppp-body interactions. At specific interaction strengths of the model, we establish an exact Floquet interaction order-range\textit{order-range}order-range mapping: the Floquet evolution operator of the ppp-body Ising model is exactly mapped to a two body Ising model with interactions having maximum range p−1p-1p−1 and exactly determined couplings. Upon further tuning the kicking strength, the mapped model becomes dual-unitary, thus providing an explicit family of ppp-body dual unitary models. We then determine exact entanglement dynamics of the ppp-body model for a class of solvable initial states at all times. We further illustrate the nontrivial structures that can emerge from the order-range\textit{order-range}order-range mapping using a minimal example of p=3p=3p=3 and generalize it for all odd ppp. These findings provide a systematic route to constructing and studying ppp-body dual-unitary Floquet models.
We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension q=2q=2q=2) to higher local dimensions (q>2q > 2q>2). We identify the existence of ''dual-unitary'' points where the model's space-time duality allows for exact analytical solutions. Our analysis reveals that while a few unique dual-unitary points exist analytically for systems with local dimensions q=3q=3q=3 and q=4q=4q=4, such points do not exist for q≥5q \ge 5q≥5 due to the lack of a unique kicking strength that satisfies the required matrix element conditions. Utilizing the transfer matrix method and a replica trick specifically adapted for higher dimensions, we derive exact expressions for the growth of entanglement entropy in the q=3q=3q=3 (kicked Potts-type) model starting from a class of solvable initial states. Our results demonstrate that at the dual-unitary point, both Rényi and von Neumann entanglement entropies grow linearly with time until reaching a maximum value determined by the subsystem size.
Abstract Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys. 49 112104) and in the q → ∞ limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity 34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.