Bosonic many-body theory of quantum spin ice

We carry out an analytical study of quantum spin ice, a U(1) quantum spin liquid close to the classical spin-ice solution for an effective spin-1/2 model with anisotropic exchange couplings J(zz), J(+/-), and J(z +/-) on the pyrochlore lattice. Starting from the quantum rotor model introduced by Savary and Balents [Phys. Rev. Lett. 108, 037202 (2012)], we retain the dynamics of both the spinons and gauge field sectors in our treatment. The spinons are described by a bosonic representation of quantum XY rotors, while the dynamics of the gauge field is captured by a phenomenological Hamiltonian. By calculating the one-loop spinon self-energy, which is proportional to J(z +/-)(2), we determine the stability region of the U(1) quantum spin-liquid phase in the J(perpendicular to)/J(zz) versus J(z perpendicular to)/J(zz) zero-temperature phase diagram. From these results, we estimate the location of the boundaries between the spin-liquid phase and classical long-range ordered phases.