# Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification

## TL;DR

This paper investigates the spectrum and classification of U(1) quantum spin liquids in pyrochlore ice systems, highlighting the quantum magnetic monopole excitations and their experimental signatures in neutron scattering.

## Contribution

It predicts the magnetic monopole continuum's enhanced spectral periodicity and provides a classification scheme for symmetry-enriched U(1) spin liquids based on monopole and spinon fractionalization.

## Key findings

- Magnetic monopoles exhibit a dual π flux background.
- Monopole continuum shows enhanced spectral periodicity.
- Predictions align with existing data on Pr2TM2O7 and Tb2TM2O7.

## Abstract

We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike the spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analogue. We further point out that the "magnetic monopole" experiences a background dual "$\pi$" flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond lattice. We then predict that the "monopole" continuum has an enhanced spectral periodicity. This prediction can be examined among the existing data on the non-Kramers doublet spin liquid candidate materials like Pr$_2$TM$_2$O$_7$ and Tb$_2$TM$_2$O$_7$ (with TM = "transition metal"). The application to the Kramers doublet systems and numerical simulation is further discussed. Finally, we present a general classification of distinct symmetry enriched U(1) quantum spin liquids based on the translation symmetry fractionalization patterns of "monopoles" and "spinons".