Families of quasi-local conservation laws and quantum spin transport

TL;DR

This paper develops a method to construct families of quasi-local operators in integrable quantum chains, improving the understanding of spin transport properties, specifically the high-temperature spin Drude weight in the XXZ chain.

Contribution

It introduces a general procedure for defining quasi-local conservation laws in integrable quantum chains, enhancing the analysis of quantum spin transport.

Findings

Constructed a continuous family of quasi-local operators for the XXZ chain.

Provided improved rigorous estimates for the high-temperature spin Drude weight.

Demonstrated the applicability of the method to deformed symmetry quantum chains.

Abstract

For fundamental integrable quantum chains with deformed symmetries we outline a general procedure for defining a continuous family of quasi-local operators whose time-derivative is supported near the two boundary sites only. The program is implemented for a spin 1/2 XXZ chain, resulting in improved rigorous estimates for the high temperature spin Drude weight.