Macroscopic entanglement in strongly correlated superconductors

A central theme in strongly correlated electron systems, as well as quantum information theory, is the concept of macroscopic quantum entanglement which can be manifested in the form of symmetry protected topological order and deconfined gauge theories. In this talk, I will present recent analytical advance in two toy models of deconfinement in the presence of fermionic matter. First, I will discuss an asymptotically soluble limit of fermions in Z2 gauge theories – Kitaev’s toric code coupled to fermionic matter fields. This model displays deconfinement and a small to large Fermi surface transition. It thereby serves as the starting point for the controlled, diagrammatic inclusion of integrability breaking terms, and thus for the derivation of the critical theory at the deconfinement-confinement transition. Second, I will discuss a frustrated Kondo impurity (an antiferromagnetic trimer) in light of the deconfinement paradigm. Apart from a trivial local Fermi liquid, I will show that this model hosts a three-channel Kondo phase which displays analogies to symmetry protected topological order. Moreover, I will explicitly derive the critical theory of the ``deconfinement’’ quantum phase transition, which is driven by instanton (``vison’’) proliferation. While both toy models were conceived under the premise of analytical tractability, I will discuss their relevance to solid state, quantum information and numerical experiments.