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The mp-ioverlap command calculates the overlap between two iMPS (ie, largest eigenvalue of the mixed transfer matrix).


mp-ioverlap [options] <psi1> [psi2]

calculates the largest eigenvalue of the mixed transfer operator {$d$}, giving the overlap of the wavefunctions as {$\braket{\mbox{psi}}{\mbox{psi2}} = d^L$}, where {$L$} is the number of unit cells.



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-c, --cart

Show the results in cartesian coordinates

-p, --polar

show the results in polar coordinates

-r, --real

Show the real part of the result

-i, --imag

show the imaginary part of the result

-m, --mag

Show the magnitude part of the result

-a, --ard

show the argument part of the result


show the argument in radians

-x, --corr

show the equivalent correlation length ({$-1/\ln \lambda$})


Rotate psi1 N sites to the right


Parity-reflect psi1


Complex-conjugate psi1


Use the string operator Op (must be a ProductMPO) to calculate {$\bigbraket{\mbox{psi1}}{\mbox{Op}}{\mbox{psi2}}$}


calculate the overlap in this quantum number sector (can be used more than once)

-s, --sort

order the quantum number sectors by magnitude


This command obtains the largest eigenvalue of the (mixed) transfer matrix between the two wavefunctions (and optional string operator). The transfer matrix is a scalar operator with respect to the global symmetries of the wavefunctions, and hence is block-diagonalized into quantum number sectors.

Generally we want to find the largest overlap. However this is quantum number dependent - by default all quantum number sectors are listed, but the -q option can be used to select just one or more quantum number sectors. Wavefunction orthonormality implies that the overlap of a wavefunction with itself is always 1.0 in the identity quantum number sector.

Note: for two unrelated wavefunctions (even if they represent the same physical state), it is in general not predictable which quantum number sector will have the largest overlap; it is necessary to check all of them.


  1. example 1
  2. example 2


  1. Previous versions applied reflection/conjugation to psi2 -- this was changed to better support inhomogeneous unit cells.

See also

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Page last modified on October 13, 2017, at 07:18 AM