Conserved Charges of Series of Solvable Lattice Models

An infinite number of solvable Hamiltonians, including the transverse Ising chain, the XY chain with an external field, the cluster model with next-nearest-neighbor x-x interactions, or with next-nearest-neighbor z-z interactions, and other solvable models that can be mapped to the free fermion system are considered. All the conserved charges of these models written by the string-type products of the interactions are obtained. In the case of the transverse Ising chain, all the known charges are rederived, and in the case of the other models, new conserved charges are obtained.