Using exact numerical studies of a few particles, the quantum melting of the Wigner crystal is revisited in two dimensions. The existence of an intermediate supersolid phase is suggested between the Fermi liquid and the Wigner crystal. The difference between lattice and continuum descriptions is clarified.
The Fermi liquid-Wigner crystal transition in a two-dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum Monte Carlo calculations. Recently, we proposed [Phys. Rev. Lett. 94, 046801 (2005)] that for intermediate densities, a hybrid phase (with the symmetry of the crystal but otherwise liquidlike properties) is more stable than both the liquid and the crystal phase. Here we confirm this result both in the thermodynamic and continuum limit. The liquid-hybrid transition takes place at ${r}_{s}^{*}=31.5\ifmmode\pm\else\textpm\fi{}0.5$. We find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature. We discuss the implications of our results for various transition scenarios (quantum hexatic phase, supersolid, multiple exchange, and microemulsions) as proposed in the literature.
For intermediate values of the Coulomb energy to Fermi energy ratio rs, the ground state of a few spinless fermions confined on a two dimensional torus is the quantum superposition of a floppy Wigner molecule with delocalized vacancies and of a Fermi liquid of intersticial particles. This raises the question of the existence of an unnoticed liquid-solid phase between the Fermi liquid and the Wigner crystal for fermionic systems in two dimensions.
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/r potential. The studies of models without disorder and spin and including disorder and spin show that the electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings
Using a few electrons interacting via a U/r Coulomb repulsion on two dimensional L ×L square lattices with periodic boundary conditions and nearest neighbor hopping t, I review on results of systematic exact finite size numerical studies of the ground state as a function of the Coulomb energy to kinetic energy ratio rs=UL/(2t√πN). Studies of the persistent currents, of the magnetization, of the inter-particle spacing distributions, of a simple analytical ansatz converge towards the same conclusion: there is a new regime for intermediate values rs, where delocalized electrons co-exist with a solid Wigner molecule. The study of this new regime, first done in the presence of random potentials, is extended to the clean lattice limit. The results are consistent, for a finite size lattice, with a possibility proposed by Andreev and Lifshitz for the continuous thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles.
We consider the temperature-induced melting of a Wigner solid in one-dimensional (1D) and two-dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.