In this paper, a Bose-Hubbard extension of a Weyl semimetal is proposed that can be realized for ultracold atoms using laser assisted tunneling and Feshbach resonance technique in three dimensional optical lattices. The global phase diagram is obtained consisting of a superfluid phase and various Mott insulator phases by using Landau theory. The Bogoliubov excitation modes for the weakly interacting case have nontrivial properties (Weyl nodes, bosonic surface arc, etc.) analogs of those in Weyl semimetals of electronic systems, which are smoothly carried over to that of Bloch bands for the noninteracting case. The properties of the insulating phases for the strongly interacting case are explored by calculating both the quasiparticle and quasihole dispersion relation, which shows two quasiparticle spectra touch at Weyl nodes.
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