Exact quantum dynamics of non-translation invariant initial states in the Ising model

I will talk about a new method for calculating the quantum dynamics of spin chains that map to free fermions. The proposed method is applicable to a wide class of initial states, most of which are difficult to write in the fermionic representation. The method is based on the fact that for spins 1/2, the Osager algebra can be represented in terms of local operators. This allows you to generate a closed system of Heisenberg equations, the dimension of which is quadratic along the length of the chain.