Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion
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Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L2 towards a 1/L decay when the Coulomb energy to Fermi energy ratio \(\) increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at \(\).
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