Quantum Phase Transition to a Zigzag Wigner Crystal

We use Quantum Monte Carlo techniques to map out the phase diagram of interacting electrons in a quantum wire. Interacting quasi-one-dimensional systems provide excellent examples of quantum phase transitions that are tractable. Previous work gave a qualitative description of the phase diagram of a quasi-one-dimensional system [Meyer, Matveev, and Larkin, PRL 2007]. At low density, electrons confined to one dimension by a transverse harmonic potential form a linear one dimensional Wigner crystal; as the density increases, symmetry about the axis of the wire is broken and there is a transition to a quasi-one-dimensional zigzag crystal. We use variational and diffusion Monte Carlo to study the phase diagram of this system quantitatively.