&     &   &      & \pm1/2 \\
        -1/2  &  h   & -1/2  &        &         &       \\
              & -1/2 &  h    & -1/2   &         &        \\
              &      &       & \dots  &         &        \\
              &      &       &  -1/2  & h       & -1/2   \\
     \pm 1/2  &      &       &        & -1/2    &  h
\end{array}\right)$$ (only non-zero entries are displayed). Besides, the short-hand notations $c^{\dagger}$ and $c$ are used in  for the $M$-dimensional row and column with the entries $c_n^{\dagger}$, $c_n$, $n\in\mathcal M$.

In particular, the correlator  at $a=b=z$ takes the following form in the representation  [@18], [@22], [@23]: $$G_{j;l}^{zz}(t)=1-\frac{2}Z\Tr(c^{\dagger}_{j}c_{j}e^{-\beta H})-
\frac{2}Z\Tr(c^{\dagger}_lc_le^{-\beta H})+
\frac{4}Z\Tr(c^{\dagger}_{j}c_{j}
e^{itH}c^{\dagger}_lc_le^{-(\beta+it)H}).
\label{8}$$ In order to calculate , it is convenient to introduce the generating functional [@18]: $$\mathcal G\equiv\mathcal G(S,T\mid\lambda,\nu)=
\frac{1}Z\Tr(e^Se^{-\lambda H}e^Te^{-\nu H}),
\label{9}$$ where $\lambda$, $\nu$ are the complex parameters, $\lambda+\nu=\beta$. The quadratic operators $S\equiv c^{\dagger}{\widehat S}c$ and $T\equiv c^{\dagger}{\widehat T}c$, used in , are defined by means of the matrices $\widehat S=\diag\{S_1,S_2,\dots,S_M\}$ and $\widehat T=\diag\{T_1,T_2,\dots,T_M\}$. For instance, the last term in right-hand side of is obtained from  in the following way: $$\lim_{\substack{S_n,T_n\to0,\\n\in \mathcal M}}\,\lim_{\lambda\to-it}\,
\lim_{\nu\to\beta+it}\frac{\partial}{\partial S_j}\,
\frac{\partial}{\partial T_l}\,\mathcal G(S,T\mid\lambda,\nu).
\label{10}$$ The trace in right-hand side of  can be re-written by means of  [@18]: $$\Tr(e^Se^{-\lambda H}e^Te^{-\nu H})=
\frac12\,(\mathcal G^+_{\Fa}Z^+_{\Fa}+\mathcal G^-_{\Fa}Z^-_{\Fa}
+\mathcal 