Universität zu Köln

Herbst, Michael F., Stamm, Benjamin ORCID: 0000-0003-3375-483X, Wessel, Stefan ORCID: 0000-0002-6353-5083 and Rizzi, Matteo (2022). Surrogate models for quantum spin systems based on reduced-order modeling. Phys. Rev. E, 105 (4). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Herbst, Michael F. UNSPECIFIED UNSPECIFIED UNSPECIFIED Stamm, Benjamin UNSPECIFIED orcid.org/0000-0003-3375-483X UNSPECIFIED Wessel, Stefan UNSPECIFIED orcid.org/0000-0002-6353-5083 UNSPECIFIED Rizzi, Matteo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-675373
DOI:	10.1103/PhysRevE.105.045303
Journal or Publication Title:	Phys. Rev. E
Volume:	105
Number:	4
Date:	2022
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2470-0053
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MATRIX PRODUCT STATES; BASIS APPROXIMATION; RENORMALIZATION-GROUP; DYNAMICS Multiple languages Physics, Fluids & Plasmas; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67537