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arXiv · 2304.13587

Reduced basis surrogates for quantum spin systems based on tensor networks

Paul Brehmer·Michael F. Herbst·Stefan Wessel·Matteo Rizzi·Benjamin Stamm
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Abstract

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.

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Paul Brehmer, Michael F. Herbst, Stefan Wessel, Matteo Rizzi, Benjamin Stamm. 2023-07-12. Reduced basis surrogates for quantum spin systems based on tensor networks. https://doi.org/10.1103/physreve.108.025306

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