Dimensional transmutation of quantum monopole dynaimcs

Fractionalization is one of the most remarkable phenomena in the systems of nontrivial topological character. Magnetic monopoles in quantum spin ice (QSI) give a typical example of fractional excitations, and a keen interest is focused on their role in dynamical and transport properties of QSI candidate materials. However, due to the fractional nature of excitations, magnetic monopoles behave quite differently from conventional excitations such as magnons, and their character still remains quite elusive. In this contribution, in order to understand the nature of magnetic monopoles, we address the anisotropic limit (J± << Jz) of spin-1/2 quantum XXZ model defined on a pyrochlore lattice. In particular, we focus on the temperature region, J±^3/Jz^2 << T << J±, where the ground state spin ice manifold is still incoherent, while the monopole excitations already show coherent quantum motion. In this region, we obtained the local dynamical structure factor by the exact diagonalization of 32 site cluster [1]. The obtained spectrum shows a steep edge discontinuity at low energy attributed to the van Hove singularity of monopole spectrum, which results from the dimensional transmutation due to the coupling to background gauge field. We clarify the origin of this dimensional transmutation in terms of the state graph description, by mapping the monopole motion to a free particle Hamiltonian on a virtual Husimi cactus graph.

[1] M. Udagawa and R. Moessner, Phys. Rev. Lett. 122, 117201 (2019).