Conserved Charges of Series of Solvable Lattice Models

TL;DR

This paper systematically derives all conserved charges for a class of solvable lattice models, including well-known and new models, revealing their underlying integrable structures and symmetries.

Contribution

It provides a comprehensive method to obtain all conserved charges for various solvable lattice models, including new charges for models beyond the transverse Ising chain.

Findings

All conserved charges are expressed as string-type products of interactions.

Re-derivation of known charges for the transverse Ising chain.

Discovery of new conserved charges for other solvable models.

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.