By P.S. Dhogal
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33)). 1. 33–35 The calculation of the zz time-dependent spin correlation function is straightforward. After exploiting the Jordan-Wigner transformation we have szn (t)szn+l − szn szn+l = c†n (t)cn (t)c†n+l cn+l − c†n cn c†n+l cn+l . √ † † † Here c†n (t) = 1/ N k exp (ikn) ck (t) and ck (t) = ck exp (iΛk t). Next we have to use the Wick-Bloch-de Dominicis theorem, c†k1 ck2 c†k3 ck4 = c†k1 ck2 c†k3 ck4 − c†k1 c†k3 ck2 ck4 + c†k1 ck4 ck2 c†k3 , and to calculate the elementary contractions introducing the Fermi function nk = 1/ (1 + exp (βΛk )), c†k1 ck2 = δk1 k2 nk1 , c†k1 c†k2 = 0.