Spin Response of a Magnetic Monopole and Quantum Hall Response in Topological Lattice Models through Local Invariants and Light

Abstract:Here, we elaborate on and develop the geometrical approach introduced in K. Le Hur, Physics Reports 1104 1-42 (2025) between the magnetic monopole created from a radial field, quantum physics and topological lattice models through quantum phase transitions. We introduce an effective magnetic moment for a monopole when applying an additional source field along z-direction which also mediates the quantum phase transition. We present its relation with the transverse pumped quantum Hall current. The magnetic susceptibility can be introduced as a measure of the topological invariant i.e. it remains quantized within the topological phase until the transition. We show the relation with two-dimensional topological lattice models such as a honeycomb Haldane model in real space. We develop the theory and present a numerical analysis between local invariants in momentum space introduced from Dirac points, correlation functions and the responses to circularly polarized light. We develop the formalism for coupled-planes materials including the possibility of quantum spin Hall effect and address a relation between the Ramanujan infinite alternating series and an interface in real space with a topological number one-half.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2512.19511 [cond-mat.mes-hall]

(or arXiv:2512.19511v4 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2512.19511 Focus to learn more arXiv-issued DOI via DataCite

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