New Forms of Ergodicity Breaking in Quantum Many- Body Systems

Generic interacting quantum many-body systems are believed to thermalize under time evolution, with the late-time behavior of initial states determined solely by appropriate Gibbs ensembles. This is guaranteed by a celebrated conjecture on the eigenstates of a quantum Hamiltonian known as the Eigenstate Thermalization Hypothesis (ETH), which is a sufficient condition for the thermalization of simple initial states. All eigenstates of generic Hamiltonians were previously believed to always satisfy ETH in the absence of an extensive number of local conserved quantities. However, recent results suggest that this is not always the case. In this talk, I will present the physics of two recently discovered mechanisms of weak ergodicity breaking: quantum many-body scars and Hilbert space fragmentation. In both cases, ETH-violating eigenstates coexist with ETH-satisfying ones, and the fate of an initial state under time evolution sensitively depends on the properties of the eigenstates it has weights on, revealing the breaking of ergodicity. On the physical front, this phenomenology is crucial for understanding the results of multiple recent experiments, and I will discuss these connections. On the mathematical front, these phenomena motivate a generalization of the fundamental definition of “symmetry” in quantum many-body systems, which reveals novel unconventional symmetries possible in quantum many-body systems. I will close with a discussion of the main challenges that remain in this field.