  Complex magnetic orders in frustrated magnets may exhibit rich melting
processes when the magnet is heated toward the paramagnetic phase. We show that
one may tune such melting processes by quantum fluctuations. We consider a
kagome lattice dipolar Ising model subject to transverse field and focus on the
thermal transitions out of its magnetic ground state, which features a
$\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC)
simulations suggest that, at weak transverse field, the
$\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge
ordered phase where the lattice translation symmetry is restored while the time
reversal symmetry remains broken. By contrast, at stronger transverse field,
QMC simulations suggest the $\sqrt{3}\times\sqrt{3}$ phase melts through a
floating Kosterlitz-Thouless phase. The two distinct melting processes are
separated by either a multicritical point or a short line of first order phase
transition.

Strongly Correlated Electrons;Statistical Mechanics