Local correlations in partially dual-unitary lattice models

In recent years, substantial progress in the field of many-particle quantum chaos has been achieved due to the introduction of a new class of models and the development of appropriate mathematical methods closely related to those in the field of quantum circuits. Our research focuses on calculating the correlations between localized quantum observables in the dual unitary quantum systems of arbitrary dimension. Dual unitary models possess a remarkable property – their dynamics are invariant under changes in the spatial and temporal degrees of freedom. We consider the problem of local correlations in the D-dimensional partially-dual-unitary (only one spatial dimension is dual to the temporal dimension) lattice of kicked coupled quantum maps.

Our study revealed that non-trivial correlations exist in the partially dual-unitary model along the “light-cone” edges in the space-time grid. The correlations can be expressed in terms of a low-dimensional transfer matrix. In the fully-dual case, the correlations completely vanish after a finite number of time steps. This supports the earlier observations indicating that the fully-dual-unitary models constitute the class of maximally chaotic systems.