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i.e. minimise

\begin{displaymath}Q[\rho] = E[\rho] - \lambda N[\rho] + P[\rho] \end{displaymath}

Choose $P[\rho]$ such that:
  1. $Q[\rho]$ is minimised by the idempotent ground-state density-matrix
  2. the eigenvalue spectrum of the Hessian of $Q[\rho]$ is as narrow as possible $\rightarrow$ efficient minimisation
  3. $P[\rho]$ may be evaluated in $O(N)$ operations

Peter D. Haynes 2001-11-19