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@ARTICLE{Herbst:907253,
      author       = {Herbst, Michael F. and Stamm, Benjamin and Wessel, Stefan
                      and Rizzi, Matteo},
      title        = {{S}urrogate models for quantum spin systems based on
                      reduced-order modeling},
      journal      = {Physical review / E},
      volume       = {105},
      number       = {4},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2022-01922},
      pages        = {045303},
      year         = {2022},
      abstract     = {We present a methodology to investigate phase diagrams of
                      quantum models based on the principle of the reduced basis
                      method (RBM). The RBM is built from a few ground-state
                      snapshots, i.e., lowest eigenvectors of the full system
                      Hamiltonian computed at well-chosen points in the parameter
                      space of interest. We put forward a greedy strategy to
                      assemble such a small-dimensional basis, i.e., to select
                      where to spend the numerical effort needed for the
                      snapshots. Once the RBM is assembled, physical observables
                      required for mapping out the phase diagram (e.g., structure
                      factors) can be computed for any parameter value with a
                      modest computational complexity, considerably lower than the
                      one associated to the underlying Hilbert space dimension. We
                      benchmark the method in two test cases, a chain of excited
                      Rydberg atoms and a geometrically frustrated
                      antiferromagnetic two-dimensional lattice model, and
                      illustrate the accuracy of the approach. In particular, we
                      find that the ground-state manifold can be approximated to
                      sufficient accuracy with a moderate number of basis
                      functions, which increases very mildly when the number of
                      microscopic constituents grows—in stark contrast to the
                      exponential growth of the Hilbert space needed to describe
                      each of the few snapshots. A combination of the presented
                      RBM approach with other numerical techniques circumventing
                      even the latter big cost, e.g., tensor network methods, is a
                      tantalizing outlook of this work.},
      cin          = {PGI-8},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-8-20190808},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / PASQuanS - Programmable Atomic Large-Scale
                      Quantum Simulation (817482)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(EU-Grant)817482},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000786497300007},
      doi          = {10.1103/PhysRevE.105.045303},
      url          = {https://juser.fz-juelich.de/record/907253},
}