Local and Quasilocal Conserved Quantities in Integrable Systems

TL;DR

This paper presents a systematic method to identify all local and quasilocal conserved quantities in integrable lattice systems, revealing new conserved operators and their implications for quantum dynamics.

Contribution

It introduces a procedure to count and generate all independent conserved operators, including novel quasilocal ones, in integrable models like the Heisenberg spin chain.

Findings

Number of conserved operators grows linearly with support size M

Existence of novel quasilocal conserved quantities in all parity sectors

Quasilocal conserved operators also present in isotropic Heisenberg model

Abstract

We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators related to time-average of local operators with a support on up to M consecutive sites. As an example we study the anisotropic Heisenberg spin-1/2 chain and show that the number of independent conserved operators grows linearly with M. Besides the known local operators there exist novel quasilocal conserved quantities in all the parity sectors. The existence of quasilocal conserved operators is shown also for the isotropic Heisenberg model. Implications for the anomalous relaxation of quenched systems are discussed as well.