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Exact results on itinerant ferromagnetism and the 15-puzzle problem

Eric Bobrow, Keaton Stubis, and Yi Li
Phys. Rev. B 98, 180101(R) – Published 19 November 2018
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Abstract

We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem is extended to all nonseparable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a U Hubbard model with one hole away from the half filling on a two-dimensional honeycomb lattice or a three-dimensional diamond lattice is fully spin polarized. Furthermore, the condition of connectivity for N-component fermions is presented, and Nagaoka's theorem is also generalized to SU(N)-symmetric fermion systems on nonseparable graphs.

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  • Received 11 May 2018
  • Revised 22 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.180101

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Eric Bobrow1, Keaton Stubis2, and Yi Li1

  • 1Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
  • 2Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218, USA

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Issue

Vol. 98, Iss. 18 — 1 November 2018

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