7 Method Orbitals BF Energy (a.u. / elec.) VMC DMC-opt. Gauss. No − 0.031 849 8(1) VMC DMC-opt. Gauss.+PW No − 0.031 849 9(1) VMC VMC-opt. Gauss. No − 0.031 856 2(1) VMC Gauss.+PW No − 0.031 861 9(3) VMC Gauss.+PW Yes − 0.031 871 3(1) DMC Gauss.+PW Yes − 0.031 918 0(3) DMC Gauss.+PW No − 0.031 918 4(3) DMC VMC-opt. Gauss. No − 0.031 918 4(3) DMC DMC-opt. Gauss. No − 0.031 919 0(2) DMC DMC-opt. Gauss.+PW No − 0.031 920 1(3) TABLE II: Non-twist-averaged QMC energies for a ferromagnetic, 121-electron HEG at $^{r}$s = 30 a.u. obtained using different orbitals: crystal (Gaussian) orbitals, in which the Gaussian exponent has been optimized within VMC or DMC and “hybrid” (Gauss.+plane-wave) orbitals of the form given in Eq. (1) with the coefficients of 20 stars of G vectors optimized within VMC. The orbitals were centered on the lattice sites of a triangular crystal. VMC-optimized BF functions were used in some of the calculations. DMC energies were obtained using a time step of 1 a.u. The non-twist-averaged DMC energy of the ferromagnetic Fermi fluid at this system size and density [ − 0 . 0319354(5) a.u. per electron] is relatively low due to single-particle finite-size effects, so that, if anything, finite-size effects are expected to favor the hybrid phase. cannot, of course, rule out the existence of other types of intermediate phase. We acknowledge financial support from Jesus College, Cambridge and the UK Engineering and Physical Sciences Research Council (EPSRC). Computing resources were provided by the Cambridge High Performance Computing Service and HPCx. [1] E.P. Wigner, Phys. Rev. 46 , 1002 (1934); E.P. Wigner, Trans. Faraday. Soc. 34 , 678 (1938). [2] C.C. Grimes and G. Adams, Phys. Rev. Lett. 42 , 795 (1979). [3] E.Y. Andrei et al. , Phys. Rev. Lett. 60 , 2765 (1988); R.L. Willett et al. , Phys. Rev. B 38 , 7881 (1988). [4] P.M. Platzman and M.I. Dykman, Science 284 , 1967 (1999); P. Glasson et al. , Phys. Rev. Lett. 87 , 176802 (2001). [5] A. Ghosh et al. , Phys. Rev. Lett. 92 , 116601 (2004). [6] B. Tanatar and D.M. Ceperley, Phys. Rev. B 39 , 5005 (1989).