• View
• Edit
• Rename
• History
• Print
• Backlinks

MpExpectationOld

This tool calculates the expectation value of an operator.

Computational complexity: {$L m^3 d^2 M^2$} [*]

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 838M)
Compiled on Feb  8 2008 at 18:56:58
usage: mp-expectation [options] <psi1> <operator> [<psi2>]
Allowed options:
  --help                show this help message
  -r [ --r ]            display only the real part of the result
  -i [ --i ]            display only the imaginary part of the result
  --notempfile          don't use a temporary data file, keep everything in RAM (faster, but needs enough RAM)
  -v [ --verbose ]      extra debug output

The operator is of the form lattice:operator.

Only operators that transform as a scalar can have their expectation value taken, which therefore implies that the wavefunctions psi1 and psi2 must have the same quantum number. To get the matrix elements of other operators, use MpRme. TODO: this limitation could be relaxed for abelian quantum numbers.

By default, the result is shown in C++ complex number format "(real,imag)". The -r and -i options can be used to show only the real and imaginary parts, respectively. Both options can be used together to show the real and imaginary parts in two columns.

There is a variant of mp-expectation, named mp-expectation-conj, which calculates the expectation value {$\langle \mathrm{psi1} | O | \mathrm{psi2}^* \rangle$}.

Examples

mp-expectation groundstate lattice:H
mp-expectation psi1 "lattice:N(2)" psi2

As usual, we use quotes (" or ') to stop the shell from interpreting the brackets.

See also

• MpOverlap
• MpRme

[*] in principle, the {$d^2M^2$} can be reduced to {$dM$}, with a re-summing of loop indices. But for typical operators this won't do much, the {$d^2M^2$} is the number of non-zero matrix elements, and in practice operators are usually quite sparse.