1994/10/09 by E. H. Lieb · 2 citations
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physrevlett.73.2158
published as Phys. Rev. Lett., 73 (1994) 2158-2161 · 9 pages, EHL14/Aug/94
arxiv created 1994/10/09 · arxiv updated 2009/11/30
The conjecture is verified that the optimum, energy minimizing magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is π per square plaquette. We require \it only that the graph has periodicity in one direction and the result includes the hexagonal lattice (with flux 0 per hexagon) as a special case. The theorem goes beyond previous conjectures in several ways: (1) It does not assume, a-priori, that all plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type on-site interaction of any sign, as well as certain longer range interactions, can be included; (3) The conclusion holds for positive temperature as well as the ground state; (4) The results hold in D ≥ 2 dimensions if there is periodicity in D-1 directions (e.g., the cubic lattice has the lowest energy if there is flux π in each square face).