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Exact results on itinerant ferromagnetism and the 15-puzzle problem

Journal Article · · Physical Review B
 [1];  [2];  [2]
  1. Johns Hopkins Univ., Baltimore, MD (United States); Johns Hopkins University
  2. Johns Hopkins Univ., Baltimore, MD (United States)
+ Show Author Affiliations
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.
Research Organization:
Johns Hopkins Univ., Baltimore, MD (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
FG02-08ER46544
OSTI ID:
1484425
Alternate ID(s):
OSTI ID: 1482764
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 18 Vol. 98; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (1)

Ferromagnetism in the SU ( n ) Hubbard model with a nearly flat band journal December 2019

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Related Subjects

15-puzzle
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Nagaoka's theorem
graph theory
itinerant ferromagnetism