Known symmetry groups are insufficient to describe the various couplings among spin, charge, and spatial degrees of freedom in fermionic systems. To address this problem, we introduce spin-charge groups (SCGs), which provide a unified framework for fermionic symmetries. SCGs incorporate spin and charge operations as `internal' symmetries, spatial and temporal operations as `external' symmetries, together with their couplings and projective twists. After deriving the general group structure of SCGs, we explore their applications in concrete physical systems, including 3He superfluids, charge-4e superconductors, collinear magnets with spin-fluxes, and superconductors with coexisting magnetic orders. We show that SCGs can enforce additional band degeneracies, Chern numbers and cross spin-charge responses. Hence SCGs provide a symmetry-based route toward the classification and exploration of new phases of matter even when strong interactions are included.
@article{arxiv.2603.18125,
title = {Spin-Charge Groups for Fermions in Fluids and Crystals: General Structures and Physical Consequences},
author = {Arist Zhenyuan Yang and Zheng-Xin Liu},
journal= {arXiv preprint arXiv:2603.18125},
year = {2026}
}