Reduced basis surrogates for quantum spin systems based on tensor networks

• URL: http://arxiv.org/abs/2304.13587v3
• Date: Wed, 12 Jul 2023 11:40:08 GMT
• Title: Reduced basis surrogates for quantum spin systems based on tensor networks
• Authors: Paul Brehmer, Michael F. Herbst, Stefan Wessel, Matteo Rizzi, Benjamin Stamm
• Abstract summary: We show how a greedy strategy to assemble the reduced basis can be implemented. observables required for the computation of phase diagrams can be computed independent of the underlying Hilbert space. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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