The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one dimensional systems. In this paper we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawa's path integral method we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the non-linear response of the system. In particular we find an interaction dependent density response due to a change in the magnetic field as well as a contribution to the non-equilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.
Dynamical time-reversal and inversion symmetry breaking, dimensional crossover, and chiral anomaly in $α$-(BEDT-TTF)$_2$I$_3$
在大多数狄拉克半金属中，时间反演和反转对称性被认为在它们的稳定性中起着至关重要的作用。我们证明了这些对称性在有机导体$α$ -（BEDT-TTF）$_2$ I $_3$中的狄拉克费米子中由于强的电子关联而被打破。该系统是一个三维的第二类狄拉克半金属的相干层间隧穿制度。预测当磁场被调谐到层间隧穿方向时，在磁阻中观察到手征异常。我们的结果表明，$α$ -（BEDT-TTF）$_2$ I $_3$是一个有用的平台，探讨手征异常和强相关性和/或维数之间的相互作用。
Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
