Reduced basis surrogates for quantum spin systems based on tensor networks

PubMed, vol. 108, pp. 025306

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 Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University

   Affiliation as printed

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

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

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

   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 · Ernst Ruska Centre

   Affiliation as printed

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

   Peter Grünberg Institut (PGI-8) , 52425 Jülich , Germany

   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 ,

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

   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

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