Quantum Matter

The entanglement spectrum denotes the eigenvalues of the reduced density matrix of a region in the ground state of a many-body system. Given these eigenvalues, one can compute the entanglement entropy of the region, but the full spectrum contains much more information. I will review geometric methods to extract this spectrum for special subregions in lorentz and conformally invariant field theories (and any theory whose universal low energy physics is captured by such a field theory).

Novel phases can result from the interplay of electronic interactions and spin orbit coupling. In the first part, we discuss a simple Hubbard model for the pyrochlore iridates, whose phase diagram contains topological insulator (TI) and various magnetic phases. The latter host the novel topological Weyl semimetal, whose excitations behave like Weyl fermions. In the second part we study a novel spin liquid that was proposed to arise in the iridates, the 3D topological Mott insulator: a fractionalized TI where the neutral spinons acquire a topologically non-trivial band structure.

Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front.

The multiscale entanglement renormalization ansatz can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat spacelike boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains.