Quantum Monte Carlo study of the quasiparticle effective mass of the two-dimensional uniform electron liquid

The real-space variation quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) are used to calculate the quasiparticle energy bands and the quasiparticle effective mass of the paramagnetic and ferromagnetic two-dimensional uniform electron liquid (2D-UEL)\@. The many-body finite-size errors are minimized by performing simulations for three system sizes with the number of electrons $N=146$, 218, and 302 for paramagnetic and $N=151$ for ferromagnetic systems. We consider 2D-UEL to be within the metallic density range $1\leq r_s \leq 5$. The VMC and DMC results predict that the quasiparticle effective mass $m^*$ of the paramagnetic 2D-UEL at high density $r_s=1$ is very close to 1, suggesting that effective mass renormalization due to electron-electron interaction is negligible. We find that $m^*$ of the paramagnetic 2D-UEL obtained by the VMC and DMC methods increases by $r_s$ but with different slopes. Our VMC and DMC results for ferromagnetic 2D-UEL indicate that $m^*$ decreases rapidly by reducing the density due to the strong suppression of the electron-electron interaction.