Surrogate models for quantum spin systems based on reduced order modelling

We present a methodology to investigate phase-diagrams of quantum spin models based on the principle of the reduced basis method. It is based on constructing a low-dimensional basis built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. We propose to use a greedy-strategy to assemble the reduced basis and thus to select the parameter points where the full model is solved. Once the reduced basis is computed, observables required for the computation of phase-diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the accuracy of this approach for a geometrically frustrated antiferromagnetic two-dimensional lattice model and quantum spin model that describes a chain of excited Rydberg atoms.