The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Abstract

The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO ( 3 ) × SO ( 3 ) × U ( 1 ) symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one- and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U / 4 t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field B s 1 e → x 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N / 2 degenerate one- s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U / 4 t finite the degeneracy of the N / 2 one- s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by B s 1 L 2 / Φ 0 and the s1 effective lattice spacing by a s 1 = l s 1 / 2 π where l s 1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ 0 = 1 . Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.