Ergodicity breaking in quantum many-body systems

Ergodicity is a key ingredient in how thermodynamics emerges from microscopic descriptions of complex systems. Breaking of ergodicity, therefore, is of fundamental interest as such scenarios fall outside the conventional paradigm of statistical mechanics and thermodynamics. I will discuss two mechanisms for ergodicity breaking in the context of quantum many-body systems. The first, under the umbrella of many-body localisation, concerns how the presence of quenched randomness can provide a robust mechanism for ergodicity breaking in isolated systems. I will discuss theoretical approaches from the perspective of many-body Hilbert/Fock spaces. They shed light on the necessary conditions that stabilise such non-ergodic behaviour as well as on the nature of a phase transition between an ergodic and a localised phase. The second involves the competition between generic quantum dynamics with measurements. In this case, I will discuss how non-ergodicity is revealed in the dynamics of quantum entanglement. I will focus on a novel entanglement phase transition induced by measurements and show how they might be related to the many-body localisation transition.