Surrogate models for quantum spin systems based on reduced order modeling

• URL: http://arxiv.org/abs/2110.15665v3
• Date: Fri, 11 Mar 2022 06:19:15 GMT
• Title: Surrogate models for quantum spin systems based on reduced order modeling
• Authors: Michael F. Herbst, Stefan Wessel, Matteo Rizzi, Benjamin Stamm
• Abstract summary: We present a methodology to investigate phase-diagrams of quantum models based on the principle of the reduced basis method (RBM) We benchmark the method in two test cases, a chain of excited Rydberg atoms and a geometrically frustrated antiferromagnetic two-dimensional lattice model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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