Conserved Charges of Series of Solvable Lattice Models

TL;DR

The paper addresses local conserved quantities in solvable one-dimensional lattice systems that map to free fermions. It develops a fermionization framework that transforms a broad class of Hamiltonians, including the transverse Ising, Kitaev, XY, and cluster-type models, into free Majorana fermions and diagonalizes them. It constructs the complete set of string-type conserved charges by analyzing the kernel of the inner-derivation operator $\delta$, obtaining $2N$ independent charges in addition to two trivial ones, and re-derives known TI/XY charges while uncovering new charges for generalized interactions. The results provide a precise algebraic handle on integrability and dynamical properties in these systems, with explicit momentum-space expressions for the charges.

Abstract

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.