4.3. Spectrum calculation for 12-site one-dimeinsional Heisenberg chain model.

The Hamiltonian is given by

(4.4)\[H = J \sum_{i=0}^{11}{\bf S}_{i}\cdot{\bf S}_{i+1},\]

where

(4.5)\[{\bf S}_0 = {\bf S}_{12}.\]

The spectrum function can be calculated by following steps.

  1. Calculate the ground state.

  2. Define excitation operators in the pair.def file.

  3. Calculate spectrum function.

See the manual for details. To simply do above steps, we prepare the script file samples/tutorial_4.3/spinchain_example.py .. in https://github.com/issp-center-dev/HPhi-gallery/tree/master/Spin/HeisenbergSpectrum. In the following, we show the procedure to obtain the specrum function by using the script file.

  1. Execute the script file (spinchain_example.py)

    $ python spinchain_example.py

  2. Plot spectrum.dat by gnuplot.

    $ gnuplot
$ set yrange [0:5]
$ set pm3d map
$ splot "./spectrum.dat" using 1:2:3

    You can see the following figure, where horizontal and vertical axises correspond to the index of wave vector and frequency, respectively.

../_images/sqomega.png