Thermalization (or lack thereof) in isolated quantum systems has been a topic of great interest recently. The eigenstate thermalization hypothesis (ETH) states that generic quantum systems thermalize, while disordered systems exhibiting many body localization (MBL) are known to be a major exception. In the last few years, a new category has emerged: weak breaking of ergodicity, exemplified by so-called many-body quantum scar states. Unlike in MBL (where all eigenstates are localized, and there is a lack of thermalization in time evolution from any initial state), in quantum scarred systems, a small number of non-thermal eigenstates cause breakdown of thermalization with only some initial states. In this talk, I will first review the phenomenology of many-body quantum scars, and introduce the paradigmatic model, the PXP model (AKA the Fibonacci chain). In the later part of this talk, I will focus on a specific simple, exactly solvable model. The idea is to consider a constrained spin model defined by a certain matrix product state (MPS), and to calculate the time evolution in the constrained Hilbert space. The result is that one sees periodic orbits in the dynamics—capturing the essence of the interesting behavior in quantum scarred systems.
Note: this event will be hybrid. The live talk occurring in Loomis 276 will be simultaneously broadcast via Zoom. The Zoom link will be sent to the Graduate Student and PDRA mailing lists. If you are not on one of those lists and are interested in attending, please email Caitlin at ckengle2@illinois.edu for the link.
