Abstract
The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.
Highlights
The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell’s theory of electromagnetism to Einstein’s theory of general relativity
Pinch-point scattering has been observed in the putative quantum spin-ice Tb2Ti2O7. In this case, the experimental scattering shows pronounced butterfly-like features in the non-spin-flip (NSF) channel and the scattering in the spin-flip (SF) channel shows narrow arm-like features extending along the h111i directions of reciprocal space, neither of which features are predicted for a spin-ice
Far we have uncovered a spin-liquid described by a tensor field carrying a continuous gauge symmetry, arising in a particular limit of a realistic model for magnetism on the pyrochlore lattice (equation (1))
Summary
The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell’s theory of electromagnetism to Einstein’s theory of general relativity. We report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice These features may already have been observed in the pyrochlore material Tb2Ti2O7. Directions of reciprocal space, which we dub ‘pinch lines’ since they are extended versions of the pinch-points exhibited in spin-ice This is interesting in the light of neutron scattering results on the pyrochlore magnets Tb2Ti2O7 and Yb2Ti2O7, which show strong, sharpening features along the h111i directions of reciprocal space. Our theory is able to account for several features of the diffuse scattering observed in Tb2Ti2O7 (refs 11–13), which are unaccounted for by a theory based on a spin-ice model
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