In many ways, the more recent paradigm of “topological phases” represents a radical departure from this thinking. In the fundamental description of these phases, Hamiltonian principles are often treated as an afterthought, while other organization principles are sought in intricate properties that are directly encoded in the many-body ground state wave functions, regardless of the interactions that stabilize them: Such properties include both entanglement, as well as topological invariants that lend a certain built-in robustness to the fascinating physical behaviors of these phases.

In this talk, I will introduce an organization principle for a large class of topological phases: Entangled Pauli principles. These principles are intimately connected to model-Hamiltonians of the traditional kind, allowing construction of model-Hamiltonians where none were known before. More importantly, they can be understood as the “DNA” of the phases they describe. In particular, they allow for a simple, efficient, and totally quantum-field-theory-free way to understand and visualize the properties that may make fault-tolerant topological quantum computing possible.