{
  "id": "2110.15665",
  "version": "v3",
  "published": "2021-10-29T10:17:39.000Z",
  "updated": "2022-03-11T06:19:15.000Z",
  "title": "Surrogate models for quantum spin systems based on reduced order modeling",
  "authors": [
    "Michael F. Herbst",
    "Stefan Wessel",
    "Matteo Rizzi",
    "Benjamin Stamm"
  ],
  "categories": [
    "quant-ph",
    "cond-mat.str-el"
  ],
  "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 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-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 tantalising outlook of this work.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-03-11T06:19:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum spin systems",
      "reduced order modeling",
      "surrogate models",
      "frustrated antiferromagnetic two-dimensional lattice model",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}