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Indeed, for the one-valley 2DEG the RPA grossly overestimates χs (Ref.) and predicts a divergence at moderately low density (Ref.) which can only be ascribed to its limited accuracy. Similarly, a small but unjustified change in the correlation energy in the calculations carried out for the 2V2DEG within the classical mapping changes a χs finite and smooth at all densities in a diverging one.
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Indeed, for the one-valley 2DEG the RPA grossly overestimates χs (Ref.) and predicts a divergence at moderately low density (Ref.) which can only be ascribed to its limited accuracy. Similarly, a small but unjustified change in the correlation energy in the calculations carried out for the 2V2DEG within the classical mapping changes a χs finite and smooth at all densities in a diverging one.
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Evidently, we disregard the valley splitting predicted when going beyond the effective-mass approximation (Ref.).
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Evidently, we disregard the valley splitting predicted when going beyond the effective-mass approximation (Ref.).
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Spin polarization of the low-density three-dimensional electron gas
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Further energy gain for the four-component phase could be in principle obtained by allowing spin/valley contamination, i.e., considering a spin/valley dependent backflow. However, a systematic study exploiting this possibility (Ref.) for the unpolarized three-dimensional electron gas gave energies in error bar with ones obtained with spin-independent backflow (Ref.).
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Further energy gain for the four-component phase could be in principle obtained by allowing spin/valley contamination, i.e., considering a spin/valley dependent backflow. However, a systematic study exploiting this possibility (Ref.) for the unpolarized three-dimensional electron gas gave energies in error bar with ones obtained with spin-independent backflow (Ref.).
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Actually, the convexity of E (rs, ζ) is spoiled by the exchange term at some finite polarization ζc. However, for rs 1, correlation effects push ζc exponentially close to one, in a range 1- ζc e-β rs.
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Actually, the convexity of E (rs, ζ) is spoiled by the exchange term at some finite polarization ζc. However, for rs 1, correlation effects push ζc exponentially close to one, in a range 1- ζc e-β rs.
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The coefficients of the leading powers of rs are kept fixed to their analytical values for the crystal phase in Ref., whereas they are fitting parameters in the present work.
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