Exact results on itinerant ferromagnetism and the 15-puzzle problem

Bobrow, Eric; Stubis, Keaton; Li, Yi

doi:10.1103/PhysRevB.98.180101

Title: Exact results on itinerant ferromagnetism and the 15-puzzle problem

Journal Article · Mon Nov 19 00:00:00 EST 2018 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.98.180101· OSTI ID:1484425

Bobrow, Eric ^[1]; Stubis, Keaton ^[1];

^[1]

Johns Hopkins Univ., Baltimore, MD (United States)

Here, 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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Research Organization:: Johns Hopkins Univ., Baltimore, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-08ER46544

OSTI ID:: 1484425

Alternate ID(s):: OSTI ID: 1482764

Journal Information:: Physical Review B, Vol. 98, Issue 18; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
itinerant ferromagnetism
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Title: Exact results on itinerant ferromagnetism and the 15-puzzle problem

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