Zeeman splitting of zero-bias anomaly in Luttinger liquids

Tunnelling density of states (DoS) in Luttinger liquid has a dip at zero energy, commonly known as the zero-bias anomaly (ZBA). In the presence of a magnetic field, in addition to the zero-bias anomaly, the DoS develops two peaks separated from the origin by the Zeeman energy. We find the shape of these peaks at arbitrary strength of the electron-electron interaction. The developed theory is applicable to various kinds of quantum wires, including carbon nanotubes.