Clumping and Adiabatic Connection

The uniform electron gas for rg 30 provides a nice example of the adiabatic connection discussed in Sect. 1.3.5. As the coupling constant A turns on from 0 to 1, the ground state wavefunction evolves continuously from the Kohn-Sham determinant of plane waves to the ground state of interacting electrons in the presence of the external potential, while the density remains fixed. (One should of course regard the infinite system as the infinite-volume limit of a finite chunk of uniform background neutralized by electrons.) 

The uniform phase becomes unstable against a charge density wave of wavevector q and infinitesimal amplitude when Cs q) of (1.167) vanishes [59]. This instability for q 2kp arises at low density as a consequence of exchange and correlation. 

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