Some New Ideas on RVB States: Generalized Flux Phases

P. W. Anderson

We here propose the concept of generalized flux for the 3d one-band Hubbard model. These are phases in which a spontaneous vorticity proportional to the number of electrons develops self-consistently. Their properties are somewhat dissimilar from other RVB states.

D. Peter, Didier Mayou, M. Cyrot

Tao Li

We show the chiral d-wave RVB state on honeycomb lattice stands as a natural generalization of the staggered flux phase on square lattice. Although the state is generated from a time reversal symmetry broken mean field ansatz, it actually represents a fully symmetric spin liquid state with a positive definite wave function in the sense of Marshall sign rule for unfrustrated antiferromagnets. The evolution of the state with the parameter $Δ/χ$ follows exactly the same manner as that of the staggered flux phase on square lattice. The critical pairing strength corresponding to the $π$-flux phase is found to be $Δ/χ=\sqrt{2}$. As a result of the geometric frustration between neighboring plaquette on honeycomb lattice, a direct generalization of the U(1) staggered flux pattern on square lattice to honeycomb lattice is impossible. Replacing it is the chiral d-wave state with $Z_{2}$ gauge structure. However, this $Z_{2}$ gauge structure is found to be ineffective after Gutzwiller projection and the system does not support topological degeneracy. The chiral d-wave RVB state is also found to be a rather good variational state for the Heisenberg model on honeycomb lattice. The spin correlation of the chiral d-wave state is found to be greatly enhanced as compared to the mean field prediction.

Alain Messager, Jean‐Louis Richard

Thomas Maurice Rice

G. Baskaran, Erio Tosatti, L. YU

The RVB state is a singlet quantum liquid which can support periodic or fluid-like quantum circulation around the elementary plaquette in two dimensions. In the s + id phase there is a half flux quanta of circulation in every elementary plaquette. We show that the holons in the presence of this lattice of circulation have a two-valley structure, as opposed to "s"or "d" states, which have a single valley. Using an effective holon Hamiltonian, we study the mean-field properties of the two-valley holon condensate, and compare its energy with the single valley case. A transition from the "d" to the "s + id" state is predicted with increasing hole concentration for sufficiently large Hubbard U. Some speculations are offered about the general case of a fluid-like distribution of flux quanta.