  The paradigmatic example of a continuous quantum phase transition is the
transverse field Ising ferromagnet. In contrast to classical critical systems,
whose properties depend only on symmetry and the dimension of space, the nature
of a quantum phase transition also depends on the dynamics. In the transverse
field Ising model, the order parameter is not conserved and increasing the
transverse field enhances quantum fluctuations until they become strong enough
to restore the symmetry of the ground state. Ising pseudo-spins can represent
the order parameter of any system with a two-fold degenerate broken-symmetry
phase, including electronic nematic order associated with spontaneous
point-group symmetry breaking. Here, we show for the representative example of
orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or
a perpendicular magnetic field plays the role of the transverse field, thereby
providing a practical route for tuning appropriate materials to a quantum
critical point. While the transverse fields are conjugate to seemingly
unrelated order parameters, their non-trivial commutation relations with the
nematic order parameter, which can be represented by a Berry-phase term in an
effective field theory, intrinsically intertwines the different order
parameters.
