Stationary states and (quasi)local charges in a semi-infinite chain

Motivated by the remarkable fact that a local defect can have global effects on the dynamics of local observables after global quenches, I revisit the conserved quantities of the quantum XY model with open boundary conditions. I present two approaches to determine the local conservation laws. A direct method that relies on the diagonalization of the model and a more abstract procedure based on a correspondence between quadratic forms of fermions and block-Toeplitz-plus-Hankel operators. Specifically, I establish the conditions that the symbol of a particular class of block-Toeplitz-plus-Hankel operators must satisfy in order to commute with a given block-Toeplits. I exhibit new families of (quasi)local conservation laws and discuss some physical consequences of the results.