Local correlations in dual-unitary kicked chains

Abstract

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 $T$. Furthermore, we identify a remarkable family of dual-unitary models where an explicit information on the spectrum of $T$ 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.

8+6 pages, 6 figures

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• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Entanglement Barriers in Dual-Unitary Circuits
• Correlations and commuting transfer matrices in integrable unitary circuits
• Exact local correlations in kicked chains at light cone edges