Matrix Product Toolkit | Tools / MpInfoOld

The mp-info program shows various details of a wavefunction.

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 802)
Compiled on Dec 10 2007 at 11:40:24
usage: mp-info [options] input-wavefunction
Allowed options:
  --help                   show this help message
  -e [ --entropy ]         show the entropy at each partition
  -s [ --states ]          show the number of states at each partition
  -d [ --density-matrix ]  show the density matrix eigenvalues
  -c [ --casimir ]         show the values of the casimir invariant operators at each partition
  -l [ --limit ] arg       limit the density matrix display to N eigenvalues (implies --density-matrix)
  -b [ --localbasis ]      Show the local basis at each site
  -2 [ --base2 ]           show the entropy using base 2 instead of base e

With no options, mp-info shows the symmetry list, the target quantum number, and the number of sites in the chain. Other options show additional information about the basis states, density matrix or quantum numbers.

Examples

To see basic information about a wavefunction:

mp-info wavefunction

prints:

Symmetry list is N:U(1),Sz:U(1)
State transforms as 20,0
Number of sites = 30

To see the number of states kept at each bond, use

mp-info -s wavefunction

prints:

#bond    #dimension  #degree
    0             1        1
    1            50      176
    2            50      202
    3           100      488
    4           100      508
    5           100      496
    6           100      517
...

Similarly for the entropy (--entropy or -e), or the density matrices (--density or -d). By default, the density matrix display shows all eigenvalues of the density matrix. This can get quite large, so the --limit N option can be used to limit the display to the largest N eigenvalues.

The --localbasis option displays the quantum numbers of the local basis at every site in the wavefunction. This is maybe useful if you forget what model the wavefunction corresponds to ;)

The --casimir shows the expectation values of the casimir invariant operators associated with each symmetry, for each bond in the system. The value refers to the expectation value of the casimir for the right partition of the system. The casimir invariants are operators that commute with all elements of the group, thus they form a maximal set of commuting observables. The casimir operator for {$U(1)$} is just the number itself (eg, the particle number). For {$SU(2)$}, the casimir invariant is {$S^2 = s(s+1)$}.

Notes

Listing the number of states is very fast, because it doesn't require any computation. Obtaining the entropy, density matrix or expectation values of the casimir invariants requires the equivalent of a sweep, because the density matrix must be obtained at each partition.