# QM3 Quantum Matter meets Maths

### Quantum many-body scars: a new form of weak ergodicity breaking in constrained quantum systems

Recent experiments on large chains of Rydberg atoms [1] have demonstrated the possibility of realising one-dimensional, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of non-ergodic dynamics, such as robust periodic revivals in global quenches from certain initial states. This weak form of ergodicity breaking has been interpreted as a manifestation of "quantum many-body scars" [2], i.e., the many-body analogue of unstable classical periodic orbits of a single particle in a chaotic stadium billiard. Scarred many-body eigenstates have been shown to exhibit a range of unusual properties which violate the Eigenstate Thermalisation Hypothesis, such as equidistant energy separation, anomalous expectation values of local observables and subthermal entanglement entropy. I will demonstrate that these properties can be understood using a tractable model based on a single particle hopping on the Hilbert space graph, which formally captures the idea that scarred eigenstates form a representation of a large $\operatorname{SU}(2)$ spin that is embedded in a thermalising many-body system. I will show that this picture allows to construct a more general family of scarred models where the fundamental degree of freedom is a quantum clock [3]. These results suggest that scarred many-body bands give rise to a new universality class of constrained quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

#### See also

Papic_slides.pdf

The goal of QM3 is to discuss recent topics in quantum matter from a mathematical perspective while building bridges between the physics and mathematics communities.

Organizers: Bruno Mera, João Pimentel Nunes, José Mourão, Pedro Ribeiro, Roger Picken, Vitor Rocha Vieira
Zoom password: send an email to one of the organizers to ask for the password.