Related papers: Topological Signatures of Magnetic Phase Transitions with Majorana Fermions through Local Observables and Quantum Information

Topological Signatures of Magnetic Phase Transitions with Majorana Fermions through Local Observables and Quantum Information

URL: http://arxiv.org/abs/2506.11731v1
Date: Fri, 13 Jun 2025 12:43:34 GMT
Title: Topological Signatures of Magnetic Phase Transitions with Majorana Fermions through Local Observables and Quantum Information
Authors: Karyn Le Hur, Fan Yang, Magali Korolev,
Abstract summary: The one-dimensional (1D) $J_1-J$ quantum spin model can be viewed as a strong-coupling analogue of the Schrieffer-Su-Heeger model.<n>This model also maps onto a p-wave superconducting wire which shows a topological phase transition with the emergence of low-energy Majorana fermions.<n>This system may be realized in materials and engineered in quantum circuits, optical lattices.
Score: 2.7204116565403744
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The one-dimensional (1D) $J_1-J_2$ quantum spin model can be viewed as a strong-coupling analogue of the Schrieffer-Su-Heeger model with two inequivalent alternating Ising couplings along the wire, associated to the physics of resonating valence bonds. Similar to the quantum Ising model, which differently presents a long-range Neel ordered phase, this model also maps onto a p-wave superconducting wire which shows a topological phase transition with the emergence of low-energy Majorana fermions. We show how signatures of the topological phase transition for the p-wave superconducting wire, i.e. a half Skyrmion, are revealed through local (short-range) spin observables and their derivatives related to the capacitance of the pairing fermion model. Then, we present an edge correspondence through the edge spin susceptibility in the $J_1-J_2$ model revealing that the topological phase transition is a metal of Majorana fermions. We justify that the spin magnetization at an edge at very small transverse magnetic field is a good marker of the topological invariant. We identify a correspondence between the quantum information of resonating valence bonds and the charge fluctuations in a p-wave superconductor through our method ``the bipartite fluctuations''. This $J_1-J_2$ system may be realized in materials and engineered in quantum circuits, optical lattices.

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