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Reduced basis surrogates for quantum spin systems based on tensor networks.

Paul Brehmer1, Michael F Herbst2, Stefan Wessel1

  • 1Institute for Theoretical Solid State Physics, RWTH Aachen University, Otto-Blumenthal-Strasse 26, 52074 Aachen, Germany.

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Summary
This summary is machine-generated.

This study introduces a greedy strategy using matrix-product states to build reduced bases for quantum many-body systems. This efficiently computes quantum phase diagrams for spin-1 models.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Physics

Background:

  • Reduced basis methods aim to simplify complex quantum systems by constructing low-dimensional subspaces.
  • Investigating quantum phase diagrams requires efficient computational approaches.

Purpose of the Study:

  • To develop and implement a greedy strategy for assembling reduced bases using matrix-product states.
  • To enable efficient computation of quantum phase diagrams for various quantum many-body systems.

Main Methods:

  • A greedy algorithm is employed to select optimal parameter points for constructing the reduced basis.
  • Matrix-product state (MPS) calculations are utilized to obtain ground states for basis construction.
  • The method constructs a low-dimensional subspace from selected ground-state solutions.

Main Results:

  • The greedy strategy effectively assembles a reduced basis from MPS calculations.
  • Computational complexity for calculating observables becomes independent of the Hilbert space size.
  • The approach is demonstrated on one-dimensional quantum spin-1 models with anisotropic and biquadratic interactions.

Conclusions:

  • The developed greedy reduced basis method offers an efficient and accurate way to compute quantum phase diagrams.
  • This approach significantly reduces computational cost for analyzing complex quantum systems.
  • The method is particularly effective for one-dimensional quantum spin-1 models.