Abstract:
We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a non-trivial magnetic flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles α−, β− with holonomies h α-(A)=h β-(A)=−1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly.
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Received: 6 April 1999 / Accepted: 21 October 2000
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Aguado, M., Asorey, M. & Esteve, J. Vacuum Nodes and Anomalies in Quantum Theories. Commun. Math. Phys. 218, 233–244 (2001). https://doi.org/10.1007/s002200100390
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DOI: https://doi.org/10.1007/s002200100390