Lecturer: Lorenzo Piroli (SISSA)
Abstract: The last year has witnessed a breakthrough in the study of transport in interacting integrable systems, with the introduction of the so-called generalized hydrodynamic approach. The latter allows us to give quantitative predictions for the long-time limit in non-homogeneous settings out of equilibrium. Among these, a popular protocol has been the one of quantum quenches from initially bipartite systems: two semi-infinite halves of a one-dimensional system, initially prepared in different macroscopic states, are suddenly joined together and then left to evolve unitarily with a given Hamiltonian. At large times, the system can be locally represented by a family of space- and time-dependent stationary states, which are fully characterized by a set hydrodynamic equations. After reviewing the general ideas, I will present further developments of the theory and several recent results. I will focus in particular on the prototypical case of the XXZ spin-1/2 chain and show how the generalized hydrodynamic equations can account for a rich phenomenology depending on the specific choice of the system's parameters. A detailed discussion of transport features will be presented, including the emergence of sub-ballistic behavior in the gapped phase and of interesting universal effects in the gapless regime.
This talk is based on the following works:
L. Piroli, J. De Nardis, M. Collura, B. Bertini, and M. Fagotti, PRB 96, (2017)
B. Bertini and L. Piroli, arXiv:1711.00519 (2017)
B. Bertini, L. Piroli, and P. Calabrese, arXiv:1709.10096 (2017)