Physical manifestations of valence-bond structures in correlated systems

Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ=n−1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ, at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to (π,π), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures. Zh. éksp. Teor. Fiz. 112, 1409–1429 (October 1997)