Matrix Product Toolkit | Tools / MpiCumulant

This tool calculates the cumulants (moments) of operators.

note:this tool has been renamed to mp-imoments

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 1494)
Compiled on May 20 2015 at 02:22:41
Using Boost version 1.41.0
Copyright (c) Ian McCulloch 1999-2015 All Rights Reserved 
For license conditions email ianmcc@physics.uq.edu.au
Documentation see http://physics.uq.edu.au/people/ianmcc/mptoolkit/
usage: mp-icumulant <psi1> <operator>
Allowed options:
  --help                show this help message
  --power arg           Calculate expectation value of operator to this power [default 1]
  -p [ --print ]        Print the MPO to standard output
  -v [ --verbose ]      extra debug output (can be used more than once)

The wavefunction psi1 is the output wavefunction from MpiDmrg

An alternative, more handy way to give the power of operator is, e.g., operator^2 for the operator raising to a power of two.

Examples

For example, if you wish to calculate the second moment of Hamiltonian, your command might look like:

 
mp-icumulant psi latttice:"H^2"

This would give you a file with entries

#degree #real #imag
0 1.6653345369377e-16 1.2924697071141e-26
1 -4.0993636626404 -5.8937963814828e-13
2 -2.138255604645 1.0787815275479e-14

where the degree 2 part is the second order cumulant (variance), the degree 1 part the squared mean of Hamiltonian.

As known the definition of variance is Var(H) = <H²> - <H>², the second moment of the Hamiltonian is simply <H²> = -2.138255604645 - 4.0993636626404 for a single site.

MpiCumulant

note:this tool has been renamed to mp-imoments

Examples

See also