  We investigate the quantum phase transitions in two capacitively coupled
chains of ultra-small Josephson-junctions, with emphasis on the external charge
effects. The particle-hole symmetry of the system is broken by the gate voltage
applied to each superconducting island, and the resulting induced charge
introduces frustration to the system. Near the maximal-frustration line, where
the system is transformed into a spin-1/2 Heisenberg antiferromagnetic chain,
cotunneling of the particles along the two chains is shown to play a major role
in the transport and to drive a quantum phase transition out of the
charge-density wave insulator, as the Josephson-coupling energy is increased.
We also argue briefly that slightly off the symmetry line, the universality
class of the transition remains the same as that right on the line, still being
driven by the particle-hole pairs.
