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Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid

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Article number245145
<mark>Journal publication date</mark>24/12/2024
<mark>Journal</mark>Physical Review B: Condensed Matter and Materials Physics
Issue number24
Volume110
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC and DMC energies are obtained in the density range 1ā‰¤š‘Ÿs≤40. Single-particle and many-body finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of twist-averaged energies to the thermodynamic limit of infinite system size. System-size-dependent errors in Slater-Jastrow-backflow DMC energies caused by partially converged VMC energy minimization calculations are discussed. We find that, for 1ā‰¤š‘Ÿs≤5, optimizing the backflow function at each twist lowers the twist-averaged DMC energy at finite system size. However, nonsystematic system-size-dependent effects remain in the DMC energies, which can be partially removed by extrapolation from multiple finite system sizes to infinite system size. The DMC energies in the thermodynamic limit are used to parametrize a local spin density approximation correlation functional for inhomogeneous electron systems. Our zero-temperature phase diagram shows a single transition from a paramagnetic fluid to a hexagonal Wigner crystal at š‘Ÿs=35⁢(1), with no region of stability for a ferromagnetic fluid.