Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions

Abstract

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.

13 pages, 8 figures; v2: minor revision

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• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Front dynamics and entanglement in the XXZ chain with a gradient
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Lindblad dynamics of the quantum spherical model
• Emergent transport in a many-body open system driven by interacting quantum baths
• Meta-conformal algebras in $d$ spatial dimensions