 94309 Lieb, E. H.
 THE FLUX PHASE OF THE HALFFILLED BAND
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Oct 9, 94

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Abstract. The conjecture is verified that the optimum, energy minimizing magnetic
flux for a halffilled band of electrons hopping on a planar, bipartite
graph is $\pi$ 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, apriori, that all plaquettes have the same flux (as in
Hofstadter's model); (2) A Hubbard type onsite 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 $D \geq 2$ dimensions if there is
periodicity in $D1$ directions (e.g., the cubic lattice has the lowest
energy if there is flux $\pi$ in each square face). \smallskip}
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