Quantum Integrals of Motion for the Heisenberg Spin Chain

TL;DR

This paper provides explicit formulas for all quantum integrals of motion in the isotropic Heisenberg spin chain, expressed through polynomials in spins, offering a direct construction independent of transfer matrix methods.

Contribution

It introduces a new explicit, polynomial-based construction of quantum integrals of motion for the Heisenberg spin chain, bypassing traditional transfer matrix approaches.

Findings

Explicit formulas for all integrals of motion are derived.

The construction is independent of transfer matrix formalism.

Continuum limits are discussed for different magnetic sectors.

Abstract

An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferrromagnetic and antiferromagnetic sectors are briefly discussed.