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 Letter, 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 nonlinear 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 nonequilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.

中文翻译：

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相互作用的凝聚态系统中的手性异常

手性异常是一种基本的量子力学现象，对粒子物理学和凝聚态物理学都非常重要。在QED的背景下，它表现为在存在电磁场的情况下手性对称性的破坏。还众所周知，异常的手性对称性破坏可仅通过相互作用而发生，如与一维系统相互作用的情况。在这封信中，我们研究了在相互作用的Weyl半金属的情况下，这两种异常手性对称模式之间的相互作用。使用Fujikawa的路径积分法，我们表明手性电荷连续性方程被相互作用的存在所修饰，这些相互作用可以被视为包括相互作用的量子物质产生的电场和磁场的影响。使用降维和最低Landau液位的Luttinger液体描述可以进一步理解这一点。这些影响表现在系统的非线性响应中。尤其是，我们发现由于磁场的变化以及在保持平衡值的同时对非平衡和非均匀霍尔响应的贡献，其相互作用依赖于密度响应。