Bosonization of Weyl Fermions

Seiju Ami

Hong-Yi Fan

A Weyl–Wigner quantization scheme for Fermi system which is parallel to the bosonic case is established. We prove a new theorem: Weyl ordering of Fermi operators is invariant under fermionic similar transformations. Comparing with the preceding paper,1 we see the Bose–Fermi supersymmetry in this aspect. As an application of the theorem, we construct a generalized fermionic squeezed state.

Guang-Quan Luo, Guan-Hua Huang, Zhi-Fang Xu

Weyl points exist in a fascinating topological state of matter with linear band crossings analogous to magnetic monopoles. Tremendous efforts have been devoted to investigating fermionic topological materials with Weyl points in the single-particle band dispersion. It remains elusive for realizing interaction-induced Weyl points, especially for bosons. Motivated by recent experimental progress in ultracold atoms, we propose a scheme to create Weyl points for Bogoliubov excitations of a bosonic superfluid in a three-dimensional cubic optical lattice. The unique design of the lattice leads to interaction-induced time-reversal symmetry breaking for a $p$-orbital superfluid, which in turn induces Weyl Bogoliubov excitations. Analogous to Weyl semimetals of electronic systems, the superfluid also supports topologically protected edge modes due to the bulk-boundary correspondence.

Leonardo Falco, R. Mignani