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Conserved quantities in integrable lattice models

Marcin Mierzejewski, University of Silesia, Poland

29.05.2015 at 09:00 

One expects that the long-time properties of generic systems are consistent with the Gibbs ensemble. It means that the steady states are determined by very few conserved quantities, e.g., the total energy, the total spin and the particle number. However, in the integrable models there exist a macroscopic number of local conserved quantities which can explain some anomalous relaxation and transport properties. Various studies have recently suggested that steady states of integrable systems are fully specified by these local conserved quantities. This conjecture is known as the generalized Gibbs ensemble and has been well established in systems which can be mapped on noninteracting particles. Application of this concept or its possible extension to other integrable systems relies on completeness of the set of conserved quantities. We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice models. As an example we study the anisotropic Heisenberg spin-1/2 chain. Besides the known local operators there exist novel quasilocal conserved quantities in various symmetry sectors.
Finally, we show how to extend this approach to study systems with weak integrability-breaking interaction.

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