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.
Barnes, S. E., "Flux States for the Infinite-U Limit of the Hubbard Model" (1991). Physics Articles and Papers. 73.