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arXiv · 2607.24038

Magnetic-texture winding controls fermion-parity switches in an interacting $p$-wave magnet ring

Hyun-Yong Lee
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Abstract

Coplanar magnetic spirals map locally onto uniform spin--orbit-coupled wires, but on a ring the rotating spin frame can change the electronic boundary condition. We prove, level by level in every fixed-particle-number sector, that even and odd texture windings impose boundary phases separated by half the single-electron flux period. Changing the winding by one also changes the physical pitch in inverse proportion to the circumference; a symmetric comparison removes this leading pitch correction. In the number-conserving topological phase, a global parity constraint then reverses the fermion-parity assignment of neighboring phase-winding branches. Density-matrix renormalization-group simulations show this reversal, support an Ising transition coexisting with a gapless charge mode, and relate the finite-size parity splitting to an independently calculated charge stiffness. Magnetic-texture winding thus changes the many-body spectrum through a global boundary condition that is not determined by the local band dispersion, providing a closed-geometry, number-conserving probe of topological pairing.

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Hyun-Yong Lee. 2026-07-30. Magnetic-texture winding controls fermion-parity switches in an interacting $p$-wave magnet ring. https://arxiv.org/abs/2607.24038

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