961 lines
80 KiB
Text
961 lines
80 KiB
Text
<!DOCTYPE html>
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<html lang="en" dir="ltr" prefix="content: http://purl.org/rss/1.0/modules/content/ dc: http://purl.org/dc/terms/ foaf: http://xmlns.com/foaf/0.1/ og: http://ogp.me/ns# rdfs: http://www.w3.org/2000/01/rdf-schema# schema: http://schema.org/ sioc: http://rdfs.org/sioc/ns# sioct: http://rdfs.org/sioc/types# skos: http://www.w3.org/2004/02/skos/core# xsd: http://www.w3.org/2001/XMLSchema# ">
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<head>
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<h1 class="nist-page__title">Nagaoka ferromagnetism in 3 × 3 arrays and beyond</h1>
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<div class="nist-field__item"><time datetime="2024-12-26T12:00:00Z">December 26, 2024</time>
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<div class="nist-field__item"><span class="nist-author">Yan Li</span>, <span class="nist-author">Keyi Liu</span>, <span class="nist-author">Garnett Bryant</span></div>
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<h3>Abstract</h3>
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Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism (IF) in the Hubbard model that has been studied theoretically for many years. The condition for NF, an infinite onsite Coulomb repulsion and a single hole in a half-filled band, does not arise naturally in materials, and was only realized recently for the first time in experiments on a 2 × 2 array of gated quantum dots. Atomically precise fabrication of dopant arrays in Si allows for engineering highly controllable systems with complex geometries. This makes dopant arrays a good candidate to study NF in different array geometries through analog quantum simulation. Here we present theoretical simulations done for 3 × 3 arrays and larger N × N arrays of quantum dots, and predict the emergence of different forms of ferromagnetism in different geometries. We find NF in perfect 3 × 3 arrays, as well as in N × N arrays for one hole less than half-filling. The ratio of the Hubbard on-site repulsion U to hopping t that defines the onset of NF increases as N increases, approaching the bulk limit of infinite U for large N. Additional simulations are done for geometries made by removing sites from N × N arrays. Different forms of ferromagnetism are found for different geometries. Loops show ferromagnetism, but only for three electrons. For loops, the critical U/t for the onset of ferromagnetism decreases as the loop length increases. We show that this different dependence on size for loops and N ×N arrays can be understood by a scaling argument. Our results show how analog quantum simulation with small arrays can elucidate the role of effects including wavefunction connectivity; system geometry, size and symmetry; bulk and edge sites; and kinetic energy in determining the quantum magnetism of small systems.
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<div class="nist-field__item">Physical Review B</div>
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<div class="nist-field__item">110</div>
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<div class="nist-field__item">Ferromagnetism, Electron Electron Interaction, Dopant Array</div>
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Li, Y.
|
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, Liu, K.
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and Bryant, G.
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(2024),
|
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Nagaoka ferromagnetism in 3 &#215; 3 arrays and beyond, Physical Review B, [online], https://doi.org/10.1103/PhysRevB.110.245141
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(Accessed March 4, 2025)
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If you have any questions about this publication or are having problems accessing it, please contact <a href="mailto:reflib@nist.gov" class="usa-link">reflib@nist.gov</a>.
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Created December 26, 2024, Updated January 8, 2025
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