Reduced basis surrogates for quantum spin systems based on tensor networks

With the team surrounding our previous paper on reduced-basis methods for quantum spin systems, Matteo Rizzi, Benjamin Stamm and Stefan Wessel and myself, we recently worked on a follow-up, extending our approach to tensor-network methods. Most of the work was done by Paul Brehmer, a master student in Stefan's group, whom I had the pleasure to co-supervise. Paul did an excellent job in cleaning up and extending the original code we had, which we have now released in open-source form as the ReducedBasis.jl Julia package.

The extension towards tensor-network methods and the integration with libraries such as ITensor.jl following the standard density-matrix renormalisation group (DMRG) approach, finally allows us to treat larger quantum spin systems, closer or at the level of the state of the art. In this work we demonstrate this by a number of different one-dimensional quantum spin-1 models, where our approach allowed us even to identify a few new phases, which have not been studied so far.

The full abstract of our paper reads

Within the reduced basis methods 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 matrix-product-states (MPS) calculations. Once the reduced basis has been obtained, 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-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Paul Brehmer, Michael F. Herbst, Stefan Wessel, Matteo Rizzi and Benjamin Stamm. Reduced basis surrogates for quantum spin systems based on tensor networks. (submitted). arXiv:2304.13587