Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown

TL;DR

This paper develops a criterion to identify and characterize interacting Weyl semimetals using the Green's function, revealing how interactions affect Weyl fermions and introducing a phase with fractionalized quasiparticles.

Contribution

It introduces a topological Hamiltonian-based criterion for interacting Weyl semimetals and explores its validity and breakdown in fractionalized phases.

Findings

Interactions can shift and renormalize Weyl points.

The criterion remains valid with long-range Coulomb interactions.

A new phase with fractionalized Weyl quasiparticles is identified.

Abstract

Weyl semimetals (WSMs) constitute a 3D phase with linearly-dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and characterize WSMs in an interacting setting using the exact electronic Green's function at zero frequency, which defines a topological Bloch Hamiltonian. We apply this criterion by numerically analyzing, via cluster and other methods, interacting lattice models with and without time-reversal symmetry. We identify various mechanisms for how interactions move and renormalize Weyl fermions. Our methods remain valid in the presence of long-ranged Coulomb repulsion. Finally, we introduce a WSM-like phase for which our criterion breaks down due to fractionalization: the charge-carrying Weyl quasiparticles are orthogonal to the electron.