Fig. 6: Application to 2D magnetic materials.
From: Programmable simulations of molecules and materials with reconfigurable quantum processors
a, Properties of extended materials can also be investigated using our quantum simulation framework. As an example, we study the square-lattice ferromagnetic (J > 0) Heisenberg model \({H}_{{\rm{2D}}}=-J{\sum }_{\langle ij\rangle }{\hat{{\bf{s}}}}_{i}\cdot {\hat{{\bf{s}}}}_{j}\). By preparing the polarized ground state \(\left\vert S\right\rangle ={\left\vert 0\right\rangle }^{\otimes N}\), applying a single-site perturbation R = X0 on the central site and measuring the system in the X basis after time evolution, we can estimate the single-particle Green’s function \(G({\bf{r}},t)=\left\langle S\right\vert {X}_{{\bf{r}}}(t){X}_{{\bf{0}}}\left\vert S\right\rangle\). Therefore we select O = Xr for various positions r as the observables in equation (7), all of which are diagonal in the measurement basis. We visualize the real part of G(r, t), where the plotted intensity and colour denotes the magnitude and sign, respectively, at Jt = 0, 0.5 and 1.0. b, The structure of excited states is extracted by classical processing of these measurements. Even though the spectrum is continuous, additional structure can be identified by computing the momentum-resolved density of states \({D}^{{P}_{{\bf{k}}}}(\omega )\), where Pk is a projector onto plane-wave states (Methods). Restricting to ky = 0 and evolving to maximum time \(J{T}_{\max }=8.0\), we see \({D}^{{P}_{{\bf{k}}}}(\omega )\) forms a band-like structure, from which a peak ω can be estimated for each k (black line). c, This peak extraction allows us to directly estimate the single-particle dispersion ω(k) across the 2D Brillouin zone.
