  Employing the self-learning quantum Monte Carlo algorithm, we investigate the
frustrated transverse-field triangle-lattice Ising model coupled to a Fermi
surface. Without fermions, the spin degrees of freedom undergoes a second-order
quantum phase transition between paramagnetic and clock-ordered phases. This
quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to
the (2+1)D XY universality class. In the presence of fermions, spin
fluctuations introduce effective interactions among fermions and distort the
bare Fermi surface towards an interacting one with hot spots and Fermi pockets.
Near the QCP, non-Fermi-liquid behavior are observed at the hot spots, and the
QCP is rendered into a different universality with Hertz-Millis type exponents.
The detailed properties of this QCP and possibly related experimental systems
are also discussed.
