From Dirac Semimetals to Topological Phases in Three Dimensions: A Coupled-Wire Construction

Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symmetries such as lattice translation, (screw) rotation, and time reversal. In this paper, we discuss many-body interactions in these systems. We focus on strong interactions that preserve symmetries and are outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a model based on a three-dimensional array of coupled Dirac wires, we show (1) the Dirac (semi)metal can acquire a many-body excitation energy gap without breaking the relevant symmetries, and (2) interaction can enable an anomalous Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the single-body setting and can only be present holographically on the boundary of a four-dimensional weak topological insulator. Both of these topological states support fractional gapped (gapless) bulk (respectively, boundary) quasiparticle excitations.