From pinch points to pinch lines: a new spin liquid on the pyrochlore lattice

One of the most fascinating disoveries in the study of spin liquids has been the existence of emergent gauge fields arising out of a disordered magnetic ground state. The best known example is provided by the spin ice pyrochlores Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, whose underlying gauge structure is revealed by the presence of pinch-point singularities in the neutron scattering response. Here we report the discovery of a new spin liquid on the pyrochlore lattice, the low temperature fluctuations of which are naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins a novel form of spin correlations, giving rise to ``pinch-line'' singularities- line-like analogues of the pinch-point singularity extending along the $\langle 111 \rangle$ directions of reciprocal space. Remarkably, our theory reproduces several otherwise unaccounted for features of neutron scattering experiments on Tb$_2$Ti$_2$O$_7$.