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This tool calculates the overlap of the left reduced density matrices between two different states.

usage: mp-density-overlap <psi1> <psi2>

The wavefunctions must be defined over the same local basis, and have the same quantum number.

The output is L lines, of {$\mathrm{Tr} \; \rho^1_n \rho^2_n$} of the left reduced density matrix over {$n$} sites, for {$n=1,2,\ldots,L$}. The final line will be the overlap of the density matrix for the complete wavefunctions; since they are pure states this will be equivalent to the square of the overlap of the wavefunctions.

For non-Abelian states, this last sentence isn't quite true: The mp-toolkit regards non-Abelian wavefunctions as being equivalent to a mixed state, comprising all possible {$S^z$} values. So, a state with {$SU(2)$} quantum number {$j$} is more properly considered as a {$(2j+1)\times(2j+1)$} density matrix with {$1/(2j+1)$} on the diagonal. Thus, {$\mathrm{Tr} \; \rho = 1$}, but {$\mathrm{Tr} \; \rho^2 = \frac{1}{2j+1}$}.

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Page last modified on July 04, 2007, at 02:30 AM