Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas N. D. Drummond and R. J. Needs TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter $^{r}$s = 31(1) a.u. and a transition to a ferromagnetic crystal at $^{r}$s = 38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic “hybrid” phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94 , 046801 (2005)]. PACS numbers: 71.10.Ca, 71.10.Pm The two-dimensional (2D) homogeneous electron gas (HEG) is one of the most important model systems in condensed-matter physics. It is our basic model of the conduction electrons in layered semiconductor devices, and consists of a set of electrons moving in 2D in a uniform, inert, neutralizing background. At high densities the HEG exists in a Fermi fluid phase, but at low densities it forms a Wigner crystal to minimize the electrostatic repulsion between the electrons [1]. Classical 2D Wigner crystals can be produced in the laboratory by spraying electrons onto droplets of liquid He [2], and quantum Wigner crystals can be formed at the interface between two semiconductors [3]. As well as being objects of fundamental scientific interest, 2D Wigner crystals may be of use in quantum computing devices [4]. At high densities the fluid ground state is paramagnetic, but at low densities this phase is unstable to a ferromagnetic fluid. There is some experimental evidence that a ferromagnetic fluid is stable at densities between the paramagnetic fluid and crystal phases [5], but these data are not conclusive. Previous theoretical studies [6, 7] have reported a region of stability for the ferromagnetic fluid. However, the energy differences between the various phases are small, and highly accurate calculations are required to resolve them. Another issue of recent interest is the possible existence of intermediate phases in the vicinity of the fluid–crystal transition [8–11]. In this paper we address the issues of the stability of the ferromagnetic fluid, the fluid–crystal transition, the magnetic behavior of the crystal, and the possibility of a “hybrid” phase of the type proposed in Ref. [11]. arXiv:1002.2101v1 [cond-mat.mes-hall] 10 Feb 2010