The Structure of Conserved Charges in Open Spin Chains

TL;DR

This paper analyzes the structure of conserved charges in integrable open XYZ spin chains, revealing differences from periodic chains, especially in the types and number of charges, with explicit results for specific models.

Contribution

It characterizes the structure of conserved charges in open XYZ spin chains, highlighting differences from periodic chains and providing explicit formulas for certain models.

Findings

Open chains have half as many conserved charges as closed chains.

Explicit expressions for charges in the open spin-1/2 XY chain are derived.

The XXX chain charges differ from the Catalan tree pattern seen in closed chains.

Abstract

We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial boundary conditions. The general structure of these charges consists of a bulk part, whose density is identical to that of a periodic chain, and a boundary part. In contrast with the periodic case, only charges corresponding to interactions of even number of spins exist for the open chain. Hence, there are half as many charges in the open case as in the closed case. For the open spin-1/2 XY chain, we derive the explicit expressions of all the charges. For the open spin-1/2 XXX chain, several lowest order charges are presented and a general method of obtaining the boundary terms is indicated. In contrast with the closed case, the XXX charges cannot be described in terms of a Catalan tree pattern.