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:
-
- 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)
- 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. https://doi.org/10.1103/PhysRevB.98.180101
Bobrow, Eric, Stubis, Keaton, and Li, Yi. 2018.
"Exact results on itinerant ferromagnetism and the 15-puzzle problem". United States. https://doi.org/10.1103/PhysRevB.98.180101. https://www.osti.gov/servlets/purl/1484425.
@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},
url = {https://www.osti.gov/biblio/1484425},
journal = {Physical Review B},
issn = {2469-9950},
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}
}
Web of Science
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Works referencing / citing this record:
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