Description
Integrable systems, having an extensive number of conserved quantities, are typically associated with ballistic transport. This picture is theoretically justified in terms of Mazur bounds [1], or the emerging field of generalized hydrodynamics [2]. However, for systems posessing parity-type symmetries (such as spin-reversal or parity-hole) there exist generic symmetric states for which ballistic contribution to transport vanishes. Extensive numerical simulations of a parity-symmetric inhomogeneous quench in the Heisenberg XXZ model clearly indicate existence of diffusive transport in the massive regime, and super-diffusive transport with a curiously looking erf-scaling profile at the isotropic point [3]. I will discuss two theoretical approaches to rigorously establishing diffusive transport in integrable lattice systems: (i) either by implementing Mazur-like bounds on the diffusion constant in terms of local conserved quantities in nearly-parity-symmetric states [4], or (ii) exact solutions of simple interacting lattice models, such as reversible, deterministic cellular automata [5].
References
[1] E. Ilievski, T. Prosen, Comm. Math. Phys. 318, 809 (2013)
[2] O. Castro-Alvaredo, B. Doyon, T. Yoshimura, Phys. Rev. X 6, 041065 (2016)
[3] M. Ljubotina, M. Žnidarič, T. Prosen, arXiv:1702.04210
[4] M. Medenjak, C. Karrasch, T. Prosen, arXiv:1702.04677
[5] M. Medenjak, K. Klobas, T. Prosen, arXiv:1705.04636
