Mixeds-sourcery: Building many-body states using bubbles of nothing
We recently introduced the idea of s-sourcery [B. Swingle and J. McGreevy, Phys. Rev. B 93, 045127 (2016)], a general formalism for building many-body quantum ground states using renormalization-group-inspired quantum circuits. In this work, we define a generalized notion of s-sourcery that applies to mixed states and study its properties and applicability. For our examples we focus on thermal states of local Hamiltonians. We prove a number of theorems establishing the prevalence of mixed s-source fixed points, giving results for free fermion models, conformal field theories, holographic models, and topological phases. Thermal double states (also called thermofield double states) and the machinery of approximate conditional independence are used heavily in the constructions. For a large class of models we provide an information theoretic argument for the existence of a local Hamiltonian whose ground state is the thermal double state, and in some cases we construct such a Hamiltonian.