  We study the quantum phase transition of interacting electrons in quantum
wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag
arrangement using quantum Monte Carlo methods. As the density increases from
its lowest values, first, the electrons form a linear Wigner crystal; then, the
symmetry about the axis of the wire is broken as the electrons order in a
quasi-1D zigzag phase; and, finally, the electrons form a disordered
liquid-like phase. We show that the linear to zigzag phase transition is not
destroyed by the strong quantum fluctuations present in narrow wires; it has
characteristics which are qualitatively different from the classical
transition.
