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.
Highlights
Dirac and Weyl semimetals are nodal electronic phases of matter in three spatial dimensions
We focus on (i) a coupled-wire realization of a Dirac-Weylmetallic phase protected by antiferromagnetic time-reversal (AFTR) and screw twofold rotation symmetries, (ii) a set of exactly solvable interwire many-body interactions that introduces a finite excitation energy gap while preserving the symmetries, and (iii) an interaction-enabledmetallic electronic phase which is otherwise forbidden by symmetries in the single-body setting
(2) We show in principle that an AFTR symmetric massless 3D Dirac system with two Weyl fermions separated in momentum space can be enabled by many-body interactions without holographically relying on a higher-dimensional topological bulk
Summary
Dirac and Weyl semimetals are nodal electronic phases of matter in three spatial dimensions. When inversion or time-reversal symmetry is broken, nodal Weyl points can be separated in energy-momentum space Such gapless electronic phases are contemporarily referred to as Weyl (semi)metals [24,25,26,27]. We focus on (i) a coupled-wire realization of a Dirac-Weyl (semi)metallic phase protected by antiferromagnetic time-reversal (AFTR) and screw twofold rotation symmetries, (ii) a set of exactly solvable interwire many-body interactions that introduces a finite excitation energy gap while preserving the symmetries, and (iii) an interaction-enabled (semi)metallic electronic phase which is otherwise forbidden by symmetries in the single-body setting
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