What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.
What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.
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Tools /
MpDensityOverlapThis 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 {$\mathrm{Tr} \; \rho^2 = \frac{1}{2j+1}$}. |