Constraints from global symmetries of quantum ice on the planar pyrochlore lattice

Abstract

We study the low energy effective theory of spin-1/2 quantum ice on the planar pyrochlore lattice from the perspective of its global symmetries. We show that the Fourier transform of the spin operator, $S_{\text{Q}}^z$, can be expressed in terms of conserved quantities associated with a 1-form U(1) symmetry along two high-symmetry momentum paths, leading to constraints on both the static and dynamical structure factors. We also derive Lieb-Schultz-Mattis type constraints that forbid the existence of a unique gapped ground state in the low energy effective theory. Our findings also apply to the (2+1) dimensional U(1) quantum link model.

Comments: 14 pages, 7 figures, accepted by Phys.Rev.B