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

Abstract

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.

Authors:
 [1];  [1]; ORCiD logo [1]
  1. Johns Hopkins Univ., Baltimore, MD (United States)
Publication Date:
Research Org.:
Johns Hopkins Univ., Baltimore, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1484425
Alternate Identifier(s):
OSTI ID: 1482764
Grant/Contract Number:  
FG02-08ER46544
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 18; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; itinerant ferromagnetism; Nagaoka's theorem; 15-puzzle; graph theory

Citation Formats

Bobrow, Eric, Stubis, Keaton, and Li, Yi. Exact results on itinerant ferromagnetism and the 15-puzzle problem. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.180101.
Bobrow, Eric, Stubis, Keaton, & Li, Yi. Exact results on itinerant ferromagnetism and the 15-puzzle problem. United States. doi:10.1103/PhysRevB.98.180101.
Bobrow, Eric, Stubis, Keaton, and Li, Yi. Mon . "Exact results on itinerant ferromagnetism and the 15-puzzle problem". United States. doi:10.1103/PhysRevB.98.180101.
@article{osti_1484425,
title = {Exact results on itinerant ferromagnetism and the 15-puzzle problem},
author = {Bobrow, Eric and Stubis, Keaton and Li, Yi},
abstractNote = {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.},
doi = {10.1103/PhysRevB.98.180101},
journal = {Physical Review B},
number = 18,
volume = 98,
place = {United States},
year = {Mon Nov 19 00:00:00 EST 2018},
month = {Mon Nov 19 00:00:00 EST 2018}
}

Journal Article:
Free Publicly Available Full Text
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