Spin - Polarization transition in the two dimensional elec - tron gas

– We present a numerical study of magnetic phases of the 2D electron gas near freezing. The calculations are performed by diffusion Monte Carlo in the fixed node approximation. At variance with the 3D case we find no evidence for the stability of a partially polarized phase. With plane wave nodes in the trial function, the polarization transition takes place at rs = 20, whereas the best available estimates locate Wigner crystallization around rs = 35. Using an improved nodal structure, featuring optimized backflow correlations, we confirm the existence of a stability range for the polarized phase, although somewhat shrunk, at densities achievable nowadays in 2 dimensional hole gases in semiconductor heterostructures . The spin susceptibility of the unpolarized phase at the magnetic transition is approximately 30 times the Pauli susceptibility. Quantum simulations show that the three–dimensional electron gas undergoes a continuous spin-polarization transition, upon decreasing the density into the strongly correlated regime, before forming a Wigner crystal [1, 2]. Despite the theoretical interest of a simple model exhibiting quantum phase transitions [3], the difficulty of realizing a low density electron gas in real materials makes the contact with experiment a rather indirect one [4]. However, electrons can be confined into effectively two–dimensional systems, for instance in Si MOSFET’s and III-V semiconductor heterostructures [5], over a density range extending down to the freezing transition [6]. Far from being a mere playground for testing many–body theories and numerical simulations, strongly correlated two–dimensional electronic systems offer an extremely rich and interesting phenomenology, such as the fractional quantum Hall effect [7] and a previously unexpected metal–insulator transition [8], not to mention their relevance to superconductor cuprates [9]. Therefore, we think that it is useful to extend the work of ref. [2] and study the polarization transition of the two–dimensional electron gas (2DEG). In fact, spin fluctuations appears to play an important role in the 2DEG at the metal–insulator transition in presence of disorder [10]).