Anomaly Non-renormalization in Interacting Weyl Semimetals

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Field Theory

Background:

• Weyl semimetals are 3D materials with unique electronic properties, featuring Weyl nodes.
• These systems exhibit emergent Weyl fermion behavior in the infrared limit.
• Understanding their response to external stimuli, especially under interactions, is key.

Purpose of the Study:

• To investigate the quadratic response of quasi-particle flow in interacting 3D lattice Weyl semimetals.
• To determine if this response is universal and independent of interaction specifics.
• To establish a non-perturbative proof of universality for the chiral anomaly on a lattice.

Main Methods:

• Analysis of interacting 3D lattice models for Weyl semimetals.
• Application of constructive bounds for Euclidean ground state correlations.
• Utilizing lattice Ward Identities to prove universality.

Main Results:

• The quadratic response of quasi-particle flow between Weyl nodes is proven to be universal.
• This universality is independent of the strength and form of interactions.
• The Adler-Bardeen non-renormalization property of the chiral anomaly is confirmed non-perturbatively on a lattice.

Conclusions:

• The study establishes a fundamental universal property of interacting Weyl semimetals.
• This universality holds even near the critical point where relativistic descriptions fail.
• The findings provide a robust theoretical framework for understanding chiral anomalies in realistic condensed matter systems.