Figure 5
![Figure 5](http://media.springernature.com/full/springer-static/image/art%3A10.1140%2Fepjqt%2Fs40507-015-0021-5/MediaObjects/40507_2015_21_Fig5_HTML.gif)
Probability \(\pmb{Pijk}\) for each state \(\pmb{|ijk\rangle}\) in the Hubbard model with three fermionic modes. The physical parameters used are hopping \(h=1\), together with (a) \(U=1\) and number of Trotter steps \(n=4\), (b) \(U=1\) and \(n=10\), (c) \(U=0.5\) and \(n=4\), and (d) \(U=0.5\) and \(n=10\). The initial state is in all cases \((|011\rangle+ |101\rangle)/\sqrt{2}\). Dashed lines refer to numerical solutions without Trotter approximation, and solid lines to numerical solutions with Trotter approximation.