  Quantum fluctuations of periodic domain-wall arrays in two-dimensional
incommensurate states at zero temperature are investigated using the elastic
theory in the vicinity of the commensurate-incommensurate transition point.
Both stripe and honeycomb structures of domain walls with short-range
interactions are considered. It is revealed that the stripes melt and become a
stripe liquid in a large-wall-spacing (low-density) region due to dislocations
created by quantum fluctuations. This quantum melting transition is of second
order and characterized by the three-dimensional XY universality class.
Zero-point energies of the stripe and honeycomb structures are calculated. As a
consequence of these results, phase diagrams of the domain-wall solid and
liquid phases in adsorbed atoms on graphite are discussed for various
domain-wall masses. Quantum melting of stripes in the presence of long-range
interactions that fall off as power laws is also studied. These results are
applied to incommensurate domain walls in two-dimensional adsorbed atoms on
substrates and in doped antiferromagnets, e.g. cuprates and nickelates.
