Title: From Dirac semimetals to topological phases in three dimensions: a coupled wire construction,
Abstract: 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 manuscript, 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 (resp. boundary) quasiparticle
excitations.