Majorana modes in long-range quantum spin models are mapped to knots and links, with eigenstate curves forming links in gapped phases and knots in gapless phases, characterized by crossing and linking numbers.
(7) The ground state phase diagram is obtained using ϵ± kc = 0, where the energy band gap closes
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Knot Topology in Quantum Spin System
Majorana modes in long-range quantum spin models are mapped to knots and links, with eigenstate curves forming links in gapped phases and knots in gapless phases, characterized by crossing and linking numbers.