Derivation of the low- T phase diagram of LiHox Y1-x F4: A dipolar quantum Ising magnet

The LiHox Y1-x F4 compound is widely considered to be the archetypal dipolar quantum Ising system, with longitudinal dipolar interactions V ij zz between Ho spins { i,j } competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the Ho concentration x, the typical strength V0 of V ij zz can be varied over many orders of magnitude, and so can the transverse field H. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, which is valid at low and intermediate temperatures. For any such dipolar quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength A0 < V0: One must therefore go beyond an electronic transverse field quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field H, temperature T, and dipole concentration x. For LiHox Y1-x F4 we predict a re-entrant critical field as a function of x. We also predict the phase diagram for x=0.045 and the behavior of the system in magnetic-resonance and muon-spin-relaxation experiments.