The Anatomy of Quantum Many-Body Scars: Origins and Implementations

Quantum many-body scars (QMBS) are a mechanism for many-body interacting systems to resist thermalisation. QMBS systems host a subset of atypical, non thermal eigenstates which are responsible for coherent oscillatory dynamics when these systems are prepared in special initial states. There exist two categories of QMBS. Firstly, there are `exact scars', which arise due to spectrum generating algebras (SGA), resulting in perfect oscillations for all times. On the other hand, there exist `approximate scars', which have been observed in experiment and are responsible for decaying oscillatory dynamics. The purpose of this thesis is to explain the origin of approximate scars, make predictions of new models expected to host them, and to realise approximate scarred dynamics experimentally. We show approximate scars arise due to algebraic structures analogous to SGA. These structures are known as `broken' Lie algebras. Understanding approximate scars at the level of a Lie algebra allows us to systematically derive higher order corrections which interpolate between approximate scarring and exact scarring. In addition, for models with a single revival frequency, indicative of some su(2) algebraic structure, we introduce a complementary approach of studying embedded hypercubic structures contained within the adjacency graph of the scarred Hamiltonian. Inspired by the notions of approximate algebraic relations and embedded graph structures, we introduce a general method of constructing scarred models via kinetic constraints. Finally, by utilising the suppressed entropy growth typical of QMBS models, we implement scarred dynamics on a quantum computer.