Data associated to the paper "Reduced basis surrogates for quantum spin systems based on tensor networks"

Zenodo (CERN European Organization for Nuclear Research)

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-state 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.

Authors 5

1. Paul Brehmer

   University of Vienna

   Affiliation as printed

   University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria

2. Michael F. Herbst

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   Mathematics for Materials Modelling, Institute of Mathematics & Institute of Materials, EPFL, CH-1015 Lausanne, Switzerland

3. Stefan Weßel Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, Otto-Blumenthal-Strasse 26, 52074 Aachen, Germany

4. Matteo Rizzi

   Forschungszentrum Jülich · University of Cologne

   Affiliation as printed

   Forschungszentrum Jülich GmbH, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), 52425 Jülich, Germany

   Institute for Theoretical Physics, University of Cologne, D-50937 Köln, Germany

5. Benjamin Stamm

   University of Stuttgart

   Affiliation as printed

   Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, 70569 Stuttgart, Germany