Toy holography in dual-unitary circuits

Dual unitaries are four-legged tensors which satisfy the unitarity condition across the time as well as the space direction. These have attracted a lot of attention in the last three years. One reason being that they allow for the construction of many-body models which display quantum chaos and are analytically tractable. In this talk will present a family of dual-unitary circuits in 1+1 dimensions which constitute discrete analogs of conformal field theories. In other words, these are quantum cellular automata which are scale and Lorentz invariant. Using dual-unitary tensors we can construct tensor-network states for our (1+1) model which look like spatial slices of curved (2+1)-D discrete geometries. As usual, we define the metric distance in the bulk in terms of the entanglement at the boundary. When such boundary state evolves via our dual-unitary circuit, its associated bulk geometry evolves in a fashion that resembles general relativity. I will present all this phenomenology with lots of pictures.