The description of many-particle systems in statistical mechanics rests on the assumption of ergodicity, which is the ability of a system to explore all allowed configurations in phase space. In quantum many-body systems, statistical mechanics predicts the equilibration of a highly excited non-equilibrium state towards a featureless thermal state. In my talk, I will discuss the phenomenon of weak ergodicity breaking, which is relevant for the experimentally realized Rydberg-atom quantum simulator. I will review original studies that suggested the absence of thermalization for a few special initial conditions, related to the existence of non-thermal eigenstates known as quantum many-body scars. In the second part of my talk, I will focus on recent insights from numerical studies of energy transport, which suggest that weak ergodicity breaking is characteristic of a much larger family of eigenstates and reveals superdiffusive transport [1]. Moreover, motivated by recent experiments that implemented periodic driving [2], I will consider the problem of controlling entanglement in interacting quantum systems through periodic driving systems [3]. I will demonstrate that this approach allows for the systematic construction of Floquet models with quantum scars. To conclude, I will discuss open problems and outline promising directions for employing quantum simulators to advance our theoretical understanding of weak ergodicity breaking.
[1] M. Ljubotina, J.-Y. Desaules, M. Serbyn, Z. Papic, Phys. Rev. X 13, 011033 (2023)
[2] D. Bluvstein, et al., Science 371, 1355-1359 (2021)
[3] M. Ljubotina, B. Roos, D. Abanin, M. Serbyn, PRX Quantum 3, 030343 (2022)