In this paper, we present a homotopical framework for studying invertible gapped phases of
matter from the point of view of infinite spin lattice systems, using the framework of algebraic …

We prove that the space P (A) of pure states of a nonelementary, simple, separable, real
rank zero C⁎-algebra A has trivial homotopy groups of all orders when P (A) is equipped …

This thesis studies a pair of symmetry protected topological (SPT) phases which arise when
considering one-dimensional quantum spin systems possessing a natural orthogonal group …

This thesis aims to lay a foundation for a C∗-algebraic approach to parametrized quantum
spin systems in the thermodynamic limit. Our main physical result is the construction of a …