Correlations in Dual Unitary Quantum Circuits

I have analyzed the correlation functions on periodic chain of sites and their long time behaviors considering special unitary operators such as the dual-unitary and 2-unitary circuits. Dynamical correlation functions in dual-unitary circuits were shown to be analytically tractable in the infinite system size. Here, we fix the system size and study the properties of these circuits in the infinite time limit. We discuss the interesting features of the autocorrelation function by averaging using local unitaries. These local unitaries are drawn from a random distribution and are applied inhomogeneously across space or time. These results are directly compared to the random matrix case. Analytic results for the Partial Spectral Form Factor (PSFF) for dual unitaries in the short times are studied in this thesis and a connection to the PSFF has been found after averaging over the observables.