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Ergodicity breaking from quantum solitons to thermal first-order transitions

In this talk I will focus on out-of-equilibrium many-body quantum systems. Generic systems thermalize in accordance with the eigenstate thermalization hypothesis, erasing local memory of their initial state. Yet striking exceptions exist. Quantum many-body scars offer a weak violation, in which rare non-thermal eigenstates coexist with an otherwise thermalizing spectrum. In the first part, I will show that scarred states may act as a vacuum supporting quasi-soliton excitations, which propagate coherently on top of the scarred dynamics. I will demonstrate the existence of this phenomenon in several constrained models, arguing that our understanding of weak ergodicity breaking is far from complete. In the second part, I will discuss how ergodicity breaking may emerge near thermal first-order phase transitions in long-range models. I will conclude by outlining a broader perspective in which non-ergodic points serve as organizing centers that structure the landscape of thermalization and its timescales.