Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Topological Monopoles in Quantum Antiferromagnets

Version 1 : Received: 6 February 2019 / Approved: 7 February 2019 / Online: 7 February 2019 (12:59:37 CET)

How to cite: Azzouz, M. Topological Monopoles in Quantum Antiferromagnets. Preprints 2019, 2019020073 (doi: 10.20944/preprints201902.0073.v1). Azzouz, M. Topological Monopoles in Quantum Antiferromagnets. Preprints 2019, 2019020073 (doi: 10.20944/preprints201902.0073.v1).

## Abstract

While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a ground state. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan-Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has non-zero divergence when phonons or shear stress are present. A possible system where the present kind of monopoles could be observed is BiCu$_2$PO$_6$.

## Subject Areas

Topological monopoles; Quantum antiferromagnets; Heisenberg model; Jordan-Wigner transformation; Spin ladders; Magnetic monopoles

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