Anomaly and symmetry-charge flow in mixed states
Abstract
The -dimensional chiral anomaly is a paradigmatic exact result in quantum field theory, traditionally formulated for zero-temperature pure states where it arises from spectral flow induced by external gauge fields and captures universal ground-state properties. In mixed states, however, the participation of many states and charge exchange with the environment invalidate this mechanism. Naive extensions yield model-dependent anomaly coefficients, calling its universality into question. Here, we resolve this problem for Abelian symmetries by deriving the anomaly from an algebraic relation between the symmetry and its flux-insertion operator. We obtain symmetry-charge flow, a mixed-state generalization of spectral flow, in which an applied field redistributes statistical weight across symmetry-resolved charge sectors. Fixed solely by symmetry, the anomaly restores universality and applies to both pure and mixed states in fermionic and bosonic systems. We substantiate these results in tight-binding fermionic models with continuous symmetry and in spin models with discrete symmetries.
Cite
@article{arxiv.2604.24872,
title = {Anomaly and symmetry-charge flow in mixed states},
author = {Ze-Min Huang and Sebastian Diehl},
journal= {arXiv preprint arXiv:2604.24872},
year = {2026}
}
Comments
6+12 pages, 3 figures