Thermodynamic limit of Mazur bound on the spin stiffness of XXZ chain, using the almost-conserved Z-operator

TL;DR

This paper provides a detailed mathematical explanation of how a rigorous bound on high-temperature spin stiffness in the XXZ spin chain is established in the thermodynamic limit, using the almost-conserved Z-operator and advanced algebraic techniques.

Contribution

It offers a rigorous derivation of the Mazur bound on spin stiffness for the XXZ chain using quasi-local algebras and Lieb-Robinson bounds, expanding on previous work.

Findings

Bound on high-temperature spin stiffness established in thermodynamic limit

Use of almost-conserved Z-operator from boundary-driven Lindblad equation

Application of quasi-local algebras and Lieb-Robinson bounds

Abstract

This short note can be considered as a mathematical supplement to [Phys. Rev. Lett. 106, 217206 (2011)], namely explaining in more detail how rigorous bound on high-temperature spin stiffness is established in thermodynamic limit using the almost-conserved Z-operator resulting from solving the boundary driven Lindblad equation for the anisotropic Heisenberg (XXZ) spin 1/2 chain . No reference to techniques used in Suzuki's proofs of Mazur's bound is made, but quasi-local spin C* algebras and Lieb-Robinson bounds are invoked instead.