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Strictly speaking, the HLR phase is only defined at zero temperature, where it occurs at a fixed electron density ((Equation presented) for the clean, Gallilean invariant system). For (Equation presented) deviating from (Equation presented) and (Equation presented), composite fermions see a background magnetic field (Equation presented), and so form Landau levels. At low enough temperature, one, thus, expects to see a sequence of integer QH states of composite fermions, which correspond to a sequence of FQH states of physical electrons with (Equation presented) [86]. In our discussion, we assume that the temperature (Equation presented) is much larger than the cyclotron frequency (Equation presented) of composite fermions, so that Landau-level quantization can be neglected. At the same time, for our estimates to be correct, we need the temperature to be much lower than the gap, (Equation presented), of the paired CF phase. We expect the cyclotron frequency (Equation presented). The Fermi velocity in the HLR phase runs with energy [Eq. (2.16)] (Equation presented). When Landau levels of composite fermions form, we expect that the running of (Equation presented) will be cut off at (Equation presented). We, thus, obtain, (Equation presented). At the first-order transition from the paired CF phase to the HLR phase, (Equation presented), so (Equation presented). Thus, our calculations are legitimate as long as (Equation presented).
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