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Off-Diagonal Density Matrix Elements

In this chapter, we are going to describe the sampling of off-diagonal matrix elements using the path-integral formalism. Instead of calculating diagonal density matrix elements $\rho({\bf R},{\bf R}'={\bf R};\beta)$, for which the paths return to their starting point, we now include the possibility of open paths. Opening one path allows one the sampling of the single-particle reduced density matrix defined by,

\rho^{[1]}({\bf r}_1,{\bf r}_1') = \frac{{V^{\!\!\!\!\!\!\:^...
...{\bf r}_N \, , \,{\bf r}_1',{\bf r}_2,\ldots,{\bf r}_N)
\end{displaymath} (208)

which is related to the momentum distribution. A PIMC simulation with two open paths samples the two-particle reduced density matrix,
\rho^{[2]}({\bf r}_1,{\bf r}_2,{\bf r}_1',{\bf r}_2') = \fra...
..., , \,{\bf r}_1',{\bf r}_2',{\bf r}_3,\ldots,{\bf r}_N)
\end{displaymath} (209)

which will be used to study natural orbitals. In the following two sections, we discuss the modifications to the sampling procedure in order to deal with the open ends.


Burkhard Militzer 2003-01-15