Higher order spin interactions mediated by the substrate

<p>Raw data for the plots used in the paper. Every file has the x axis as the first column and the appropriate interaction as the second column. To obtain the same values as in the paper, normalize the second column by the hopping (t = 0.5).&nbsp;</p> <p>The expression for the fourth order expansion term was obtained using the SNEG package (http://nrgljubljana.ijs.si/sneg/) but can be handled by Mathematica.&nbsp;</p> <p>&nbsp;</p> <p>nc is the non-commutative multiplication</p> <p>&nbsp;</p> <p>Electron field operators are expressed with the following subscripts:</p> <p>c[type, site, time, spin]&nbsp;</p> <p>type: 0 - creation; 1 - annihilation</p> <p>site: from i_1 to i_4</p> <p>time: imaginary time from t_1 to t_4</p> <p>spin: 1,2,3 representing x,y,z</p> <p>&nbsp;</p> <p>Spin operators are expressed with the following subscripts:</p> <p>S[site,spin]</p> <p>site: from i_1 to i_4</p> <p>spin: 1,2,3 representing x,y,z</p>