Orateur
Description
Symmetries play a crucial role in charge transport in quantum many-body systems and can lead to striking departures from conventional diffusion. While considerable progress has been made in understanding the interplay between integrability, continuous symmetries, and anomalous transport, the role of discrete space-time symmetries remains less understood. In this talk, I will discuss integrable unitary circuits with asymmetric gates or circuit geometries and related continuous-time chiral ladder models as a setting in which these questions can be explored. The examples presented show how asymmetric circuit geometry leads to an asymmetric dynamical structure factor with symmetric charge fluctuations. Moreover, they illustrate how the Gallavotti–Cohen fluctuation symmetry can be broken in integrable systems in the absence of PT symmetry, and how its emergence may instead be tied to crystallographic symmetries. Furthermore, they show that breaking time-reversal symmetry - a symmetry absent from the KPZ equation — is not sufficient to stabilize KPZ superdiffusion in integrable systems. Together, these results illustrate the intricate role played by discrete space-time symmetries in determining charge transport and fluctuation properties of integrable many-body dynamics.