Deconfinement-confinement transition induced by chemical disorder in quantum spin ice

Spin ice is a cooperative paramagnet featuring a emergent U(1) gauge structure and fractionalized excitations. In particular, the spin structure in the Coulomb phases have been analytically understood based on the large-N approximation for Ising (N = 1) and Heisenberg (N = 3) spins. Nevertheless, its validity and the physical effects towards smearing out of the Coulomb nature requires better understanding. Here, we employ the Abelian duality transformation to explore the non-perturbative effects for N = 1. It turns out that the substantial doping in the Ising spin ice brings about the deconfinement-confinement transition. As a consequence of the non-linear mode coupling imposed by the spin length condition, there is a sharp phase transition to confined phase with disorder. We also discuss the implication of this critical point to the spin structure.