Condensed Matter Theory

Abstract:

These notes accompany lectures given in June 2025 at the summer school Fundamental Problems in Statistical Physics XVI. They offer a short introduction to random quantum circuits as simple models for generic many-body quantum systems. They give an outline of the motivation for introducing these models, starting from ideas of random matrix theory. They also provide a sketch of calculations of some of the quantities of most physical interest, based on an average over an ensemble of systems. These quantities give insights into operator spreading, entanglement dynamics and spectral correlations.

Abstract:

We construct exact strong zero mode operators (ESZM) in integrable quantum circuits and the spin-1/2 XXZ chain for general open boundary conditions, which break the bulk U(1) symmetry of the time evolution operators. We show that the ESZM is localized around one of the boundaries and induces infinite boundary coherence times. Finally we prove that the ESZM becomes spatially non-local under the map that relates the spin-1/2 XXZ chain to the asymmetric simple exclusion process, which suggests that it does not play a significant role in the dynamics of the latter.

Abstract:

We study the behavior of catalytically active droplets in multicomponent conserved mixtures affected by noise. Working in the thin interface limit, we analytically determine the state diagram of the system, characterized by multiple dynamical regimes, and verify our findings using numerical simulations. In particular, we show the emergence of a nonreciprocal, chemically mediated interaction between the droplets, which leads to the formation of (meta)stable clusters of droplets of different species. We find that the clusters can display self-propulsion in a large part of the parameter space, including regions where the nonreciprocal interactions between the droplets are purely attractive. This surprising feature arises from the nonlocal nature of the chemical interactions, and points to locality violations as a general mechanism for energy dissipation and emergence of out-of-equilibrium steady states in active matter.