Matrix Product Toolkit | Projects / KagomeStrip

The Kagome strip with SU(2) symmetry is obtained with the -H kagomoe-su2 option to mp-idmrg5. The unit cell must be a multiple of 6, and the target quantum number must be 0 (option -q 0). The SU(2) version is not capable of calculating magnetized states. The coupling coefficients are specified by --Jleg and --Jcross, for the spin-spin interaction on the outer legs, and internal crosses, respectively.

For correlation functions, use the model spin-su2.

Example script, to perform some DMRG then optimize the wavefunctions with some steps of imaginary time evolution.

#!/bin/bash

if [ $# -ne 2 ] ; then
echo "usage: doit <Jleg> <unitcell>"
exit 1
fi

jleg=$1
jcross=1
unitcell=$2
steps=10

for states in 100 200 300 400 500 600 700 800 ; do
if [ -f psi-Jleg$jleg-Jcross$jcross-m$states-u$unitcell ] ; then
mp-idmrg5 -H kagome-su2 --Jleg $jleg --Jcross $jcross -m $states -s $steps -w psi-Jleg$jleg-Jcross$jcross-m$states-u$unitcell
mp-idmrg5 -H kagome-su2 --Jleg $jleg --Jcross $jcross -m $states -s $steps -w psi-Jleg$jleg-Jcross$jcross-m$states-u$unitcell
mp-idmrg5 -H kagome-su2 --Jleg $jleg --Jcross $jcross -m $states -s $steps --evolve 0.01 -w psi-Jleg$jleg-Jcross$jcross-m$states-u$unitcell
mp-idmrg5 -H kagome-su2 --Jleg $jleg --Jcross $jcross -m $states -s $steps --evolve 0.001 -w psi-Jleg$jleg-Jcross$jcross-m$states-u$unitcell
fi
done

Get Code

correlations:

mp-icorrelation -l 26 spin-su2 S S psi > psi.corr

Bowtie field

To get the kagome lattice with a forced plaquette field, use the model kagome-field-su2. This model additionally uses the parameter kagome-cell, which specifies the periodicity of the unit cell. This must be a multiple of 6 sites. The unit cell size of the wavefunction must be a multiple of this unit cell (eg, it is possible to use kagome-cell 12 -u 24, for example). The pinning field acts on the first diamond of the unit cell.