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 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 -component fermions is presented, and Nagaoka's theorem is also generalized to -symmetric fermion systems on nonseparable graphs.
- Received 11 May 2018
- Revised 22 July 2018
DOI:https://doi.org/10.1103/PhysRevB.98.180101
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