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arXiv · 2603.18125

Spin-Charge Groups for Fermions in Fluids and Crystals: General Structures and Physical Consequences

Arist Zhenyuan Yang·Zheng-Xin Liu
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Abstract

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 $^3$He 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.

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Arist Zhenyuan Yang, Zheng-Xin Liu. 2026-03-18. Spin-Charge Groups for Fermions in Fluids and Crystals: General Structures and Physical Consequences. https://arxiv.org/abs/2603.18125

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