Non-Hermitian chiral anomalies
Abstract
The chiral anomaly underlies a broad number of phenomena, from enhanced electronic transport in topological metals to anomalous currents in the quark-gluon plasma. The discovery of topological states of matter in non-Hermitian systems raises the question of whether there are anomalous conservation laws that remain unaccounted for. To answer this question, we consider both two and four space-time dimensions, presenting a unified formulation to calculate anomalous responses in Hermitianized, anti-Hermitianized, and non-Hermitian systems of massless electrons with complex Fermi velocities coupled to non-Hermitian gauge fields. Our results indicate that the quantum conservation laws of chiral currents of non-Hermitian systems are not related to those in Hermitianized and anti-Hermitianized systems, as would be expected classically, due to different anomalous terms that we derive. We further present some physical consequences of our non-Hermitian anomaly that may have implications for a broad class of emerging experimental systems that realize non-Hermitian Hamiltonians.
- Publication:
-
Physical Review Research
- Pub Date:
- October 2022
- DOI:
- 10.1103/PhysRevResearch.4.L042004
- arXiv:
- arXiv:2106.12305
- Bibcode:
- 2022PhRvR...4d2004S
- Keywords:
-
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory
- E-Print:
- 7+16 pages, 1+5 figure