Using a one-dimensional lattice to model a finite temperature Wigner crystallization.

In this talk, we present our work on the one-dimensional Wigner crystal realized in a lattice model system. This work was motivated to provide high accuracy finite temperature electronic structure results for the 1D Wigner crystallization due to recent advances in experimentally realizing low dimension Wigner crystals, and their potential applications in quantum computing. This work is based on and inspired by work from Ostilli and Presilla on condensations in the space of states. We use a 1D lattice model of spin-polarized electrons interacting through a screened Coulomb potential, tuned by a coupling parameter. This model's Hilbert space can be partitioned into "condensed" and "normal" subspaces, where a coupling parameter crossover (g_c ) indicates a transition between the two spaces and crystallization. We investigated the behavior of the static structure factor (S(q)) and g_c, as a function of density and temperature, as crystallization indicators. We used full configuration interaction and other exact methods to investigate the behavior of S(q) and g_c in small systems. Full configuration quantum Monte Carlo (FCIQMC) and density matrix quantum Monte Carlo (DMQMC) methods were used to investigate larger systems.