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For finite doping, δ, relative to half filling, it is shown, within the confines of a mean-field auxiliary-operator formulation, for the strictly infinite-U, i.e., J=0, limit of the two-dimensional Hubbard model, that the spinons generate a fictitious magnetic flux to which holons are subject and vice versa. For small doping, a flux state is the absolute ground state and has 1-δ=2p/q, where p/q is a rational fraction and the flux per plaquette is Φ=(p/q)Φ0, where Φ0 is the flux quantum. This phenomenon can be viewed upon as an all-electron Peierls instability or as broken statistical symmetry.


S. E. Barnes, Physical Review B, 44, 801-804, 1991. "Copyright © 1991 by the American Physical Society.”

Link to the online abstract:

DOI: 10.1103/PhysRevB.44.801