Figure 10

The unequal-time thermal correlation function \(\langle O_{0}(0) O_{i}(t)\rangle \) for varying distance \(i = 1,\ldots ,5\) (shifted in magnitude for displaying purposes) at \(T/m = 1\) for \(N = 8\), where \(O_{i} = \varepsilon _{i}Z_{i-1}\otimes Z_{i}\), i.e. the relevant term of the number operator. The solid lines are the exact solutions while the crosses represent the values calculated with the Trotterized time-evolution operator (\(a\delta _{t} = 0.2\)) for the variatonal Gibbs state \(\rho _{var}\) produced with infinite statistics