Figure 9

Simulation of a 2D lattice of \(\pmb{3\times3}\) sites where the coupling ratios are: \(\pmb{U/t=2}\) , \(\pmb{U/t'=10}\) and \(\pmb{U/U'=5}\) . The principal plot shows the fidelity of the evolved state with digital methods for a phase of \(\theta\equiv U t =4\) applying different numbers of Trotter steps, l. The inset shows the population of sites 2 and 4 being the initial state \(|\Psi_{I}\rangle=b^{\dagger}_{2}|0\rangle\). The markers denote the digital evolution with 10 Trotter steps while the lines show the exact evolution.