What is the quantum ground state of dipolar spin ice?

Recent work on Dy2Ti2O7 spin ice has revealed a partial loss of residual entropy deep within the spin ice state [1]. It has been known for some time that the spin ice materials should have either magnetically ordered [2] or quantum spin liquid [3] ground states and this latest work hints at the possibility of determining them experimentally. We study a natural model for the dipolar spin ice materials and map out the entire ground state phase diagram in the presence of quantum tunneling between the ice states [4]. In the classical case, we show that the ground states in our 3D long-range interacting model can be determined from those of a short-range interacting 2D model and, remarkably, in the quantum case, only a very small tunneling coupling compared to the dipolar coupling is necessary to enter the quantum spin liquid state. \\[4pt] [1] D. Pomaranski et al., Nature Physics 9, 353-356 (2013).\\[4pt] [2] R. G. Melko, B. C. den Hertog, and M. J. P. Gingras, Phys. Rev. Lett. 87, 067203 (2001).\\[0pt] [3] M. Hermele, M.P.A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004);A. Banerjee et al., Phys. Rev. Lett. 100, 047208 (2008);N. Shannon et al., Phys. Rev. Lett. 108, 067204 (2012).\\[0pt] [4] P. McClarty et al., arXiv:1410.0451