Reduced basis modeling for quantum spin systems based on DMRG

Within the reduced basis modeling approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy-strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on density-matrix-renormalization-group (DMRG) calculations. 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 efficiency and accuracy of this approach for different one-dimensional quantum spin-S models with both S=1/2 and S=1, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.