Interacting Dirac Semimetals*

The experimental discovery of three dimensional (3d) Dirac semimetals has opened up a new world of symmetry protected gapless state with non-trivial topological properties. While most existing studies have focused on the free fermion descriptions, we will show that interaction effects will significantly change the topological classification of Dirac semimetals. With the help of the dimensional reduction technique, we explicitly show that 3d Dirac semimetals protected by C_n rotation symmetries, such as Cd3As2 and Na3Bi, can be adiabatically connected to a gapped 3d axion insulator and gapless 1d axion strings in a symmetric way. This construction demonstrates that the anomaly nature of 3d Dirac semimetals is one dimensional. We further show that the non-interacting classification of a 3d Dirac semimetal generally reduces from Z to its Z_n subgroup in the presence of strong interactions. Our work lays the theoretical foundation for strongly interacting topological semimetals and paves the way for their future material realizations.